Systems and methods for noninvasive blood glucose and other analyte detection and measurement using collision computing

ABSTRACT

In a noninvasive system for detection/measurement of glucose and other analytes in a medium such as tissue, spectra from the medium are deconstructed into features. Conditioned features, which contain frequency components specific to glucose or the other analytes, are derived from one or more features by modulating a carrier kernel with the feature. The conditioned features are computationally collided with one or more Zyotons that are co-dependent with the conditioned features. One or more collisions amplify a property of the analyte e.g., energy absorbed by glucose in tissue from radiation directed to the skin. A gradient of several values of the amplified property, each value corresponding to a particular radiation pattern according to a spectroscopic tomographic sequence, is used to select a suitable projector curve, with which a representative amplified value is projected to an accurate estimate of the concentration of glucose or the other analytes, without needing personalized calibration.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of priority to U.S. Provisional PatentApplication Ser. No. 62/057,103 entitled “A System and Method forGenerating Feature Sets Using Tomographic Spectroscopy, for AnalyteDetection,” filed on Sep. 29, 2014; and to U.S. Provisional PatentApplication Ser. No. 62/057,496 entitled “Non-Invasive GlucoseMonitoring,” filed on Sep. 30, 2014, the contents of each of which areincorporated herein by reference in their entirety.

FIELD OF THE INVENTION

In general, this disclosure relates to a system for detecting and/orquantifying the presence of very small amounts of material, the propertyor concentration of a material, or changes in the amount or propertiesof the material, or an event or anomaly of interest and, in one example,specifically to a system that performs measurement of biochemicalanalytes using diffuse reflectance tomographic spectroscopy inconjunction with collision computing.

BACKGROUND

The measurement of substances at extremely low concentrations in complexsamples has absorbed the efforts of chemists for centuries. Modernspectroscopic techniques, which allow measurement of substances atparts-per-million (ppm) or even parts-per-billion (ppb) concentrations,have revolutionized this field and allowed the detection and measurementof naturally-occurring materials such as hormones, contaminatingsubstances such as mercury, and pollutants such as atmospheric sulfurdioxide at levels far below those achieved using earlier methods ofanalysis. The direct measurement of many important substances in humantissue, however, has not been as successfully accomplished, and manyother measurements where the substance to be measured is at a lowconcentration cannot be made accurately in a high noise and/or highclutter environment. One particularly challenging problem concerns themanagement of diabetes.

Diabetes is a condition in which the body's natural control of bloodsugar (glucose) has been lost. Insulin is a hormone that is secreted bythe pancreas that works with the body to process blood sugar. Typically,diabetes is caused by some problem with the body's ability to create oruse insulin. Diabetes occurs in different medical conditions: type 1diabetes (previously known as “juvenile diabetes”), type 2 (“adultonset”) diabetes, and gestational diabetes (a complication ofpregnancy). In type 1 diabetes, the patient's pancreas is no longer ableto produce insulin at normal rates, while in type 2 and gestationaldiabetes, a patient's cells are not able to properly utilize insulin.Some patients with type 2 or gestational diabetes can treat theirconditions using diet, exercise, or a variety of pharmaceuticalpreparations. All patients with type 1 diabetes (and many with type 2,especially of longer duration) typically must control the disease withinjections or infusions of insulin.

A body's normal creation and processing of insulin generally varies overthe course of the day depending on a variety of factors, including whenand what a person eats, whether that person is exercising, and the timeof day. This variation in normal insulin production usually serves tomaintain safe glucose levels in the body. If diabetes is left untreated,the complications that can arise can be extremely serious. In theabsence of insulin, glucose in the blood can reach dangerously highlevels. Extended periods of high blood glucose levels (“hyperglycemia”)can lead to a condition known as ketoacidosis, which, if untreated, canbe fatal. Chronic poor control of glucose levels can also cause seriouslong-term complications, which include eye damage (resulting inblindness), kidney damage, cardiovascular disease, loss of feeling inthe extremities, and slow healing of wounds. Frequently, diabetes mayrequire amputations of toes, feet or legs. If blood glucose levels areallowed to drop below a threshold value (generally 50-60 milligrams perdeciliter), the person can be in acute danger from this “hypoglycemia,”which can cause confusion, difficulty speaking, unconsciousness, andcoma.

To allow better information and control, blood glucose measurementsystems that can be used by individual users have been developed. Theseblood glucose measurement systems typically require the use of anelectronic meter and disposable test strips. A test strip is insertedinto the meter, and the user pricks himself or herself (usually on afinger) with a lancet to draw a small amount of blood which is appliedto the test strip. The blood glucose meter, using one of a variety ofanalysis techniques, determines the amount of glucose in the small bloodsample drawn from the user. However, because of the pain involved inlancing a body part to draw blood, the need to dispose of materialscontaminated with blood, and the visibility and potential embarrassmentof testing using conventional blood glucose monitoring systems, manyinvestigators have tried to develop technologies that allow measurementof blood glucose without drawing blood or causing discomfort. Thesetechnologies have been termed “noninvasive” blood glucose measurementsystems, or simply “noninvasive glucose.”

For example, U.S. Pat. No. 4,655,225, issued to Dähne et al., with afiling date of Apr. 18, 1985, appears to describe a relatively simpleapproach to measuring glucose in tissue. This patent states at column 1,lines 8 through 18: “This determination is carried out by measuring theoptical near infrared absorption of glucose in regions of the spectrumwhere typical glucose absorption bands exist and computing the measuredvalues with reference values obtained from regions of the spectrum whereglucose has no or little absorption and where the errors due tobackground absorptions by the constituents of the surrounding tissues orblood containing the glucose are of reduced significance or can bequantitatively compensated.” When investigators eventually determinedthat no regions of the near-infrared NIR spectrum meeting these criteriacould be found, they employed advanced techniques, augmented withsophisticated modifications to the instrumentation and complicatedmathematical treatments. The NIR region used in these techniques istypically the region of the electromagnetic spectrum in the wavelengthrange of 700-2,500 nanometers

The most commonly-investigated technique for noninvasive glucose overthe past twenty-five years or so has been near-infrared spectroscopy(NIRS), using light that is just beyond the visible portion of thespectrum, and generally considered to be a wavelength range of about 700nanometers to about 2,500 nanometers. When near-infrared light isapplied to tissue, generally the light is both scattered by cells andstructures under the skin and is absorbed by substances in the tissue,including glucose, which can be termed an “analyte” (a substance whoseconcentration is being determined). The amount of absorbance due toglucose in this wavelength region, however, is extremely small and,coupled with (i) the low concentration of glucose in the fluids oftissue (about 50-500 milligrams per deciliter, equivalent to about 0.05%to 0.5%), (ii) the presence of many compounds with similar chemicalstructures and similar absorbance patterns in the near-infrared region,and (iii) the extremely high concentration of water in tissue, makesdirect measurement of an analyte in this region of the spectrum verychallenging, requiring the use of sophisticated spectroscopic imagingand computational techniques.

Many patents, such as U.S. Pat. No. 5,460,177, issued to Purdy, et al.in 1995, appears to describe approaches for using light from thenear-infrared portion of the spectrum to provide “expressions” orspectra that can be examined to determine the concentration of glucosewithout drawing a sample of blood. Commonly-employed data reductiontechniques in previous investigations generally include what are knownas “multivariate” techniques, such as principal component analysis(“PCA”), partial least squares (“PLS”), support vector machine (“SVM”),and multiple linear regression (“MLR”). As a group, when theseapproaches are applied to the measurement of chemical substances, theyare often referred to as “chemometrics.” These multivariate techniquesmay make it theoretically possible to create a correlation betweenmeasurable properties of a material like tissue, such as the amount oflight absorbed or reflected as a function of wavelength (known as a“spectrum”), and the concentration of an analyte such as glucose. Anexample spectrum, which plots a variable related to light intensity(such as absorbance, transmittance, energy, etc.) as a function of thewavelength of light expressed in nanometers, is shown in FIG. 1.

In order to perform a multivariate analysis on a set of data, sometechniques first build what is called a “model.” This may be done byfirst creating a number of like measurements (typically termed the“calibration set” in the context of multivariate analysis), which arespectra which contain the value of a parameter related to lightintensity as a function of wavelength and which have known values forthe concentration of the analyte. FIG. 2, for example, depicts anabsorbance spectrum for one known concentration of glucose. The overallvariance in the calibration data set may be separated into “factors”which typically represent decreasing amounts of variance. This model,once created using the multivariate technique, may represent thecontribution of a measurement at each wavelength to the concentration ofthe analyte. The values of the model at each wavelength are often termed“final regression coefficients.” At some wavelengths, the value ispositive, which may mean that the measurement at that wavelengthcontributes actual value to the calculation of the concentration, whileat other wavelengths the value is negative, which may indicate an amountto be subtracted in the concentration calculation.

Once such a model, an example of which is shown in FIG. 3, has beencreated, a spectrum with an unknown analyte concentration can beanalyzed using that model. With reference to FIG. 4, this can be done bymultiplying the value of the new spectrum at each wavelength by thevalue of the final regression coefficient of the model at the samewavelength, and adding up all the results of those multiplications togive an estimated value of the analyte. The accuracy of this estimatedconcentration value usually depends on many factors—among them: thenumber of spectra used in the calibration set, the number ofmultivariate “factors” used to construct the model, the accuracy of themeasurement process for the spectra, the similarity of theinstrumentation used to generate the spectra, and the strength of themeasured parameter. The measured parameter in the examples describedabove is the amount of absorbance of glucose molecules at each of thewavelengths, which is quite weak, and which is hidden under the strongabsorbance of other components of tissue; the absorbance spectra of sometissue components are shown in FIG. 5, but these spectra arenormalized—they are not based on a uniform scale.

Attempts at making measurements of glucose in tissue using thesetechniques have been made, but to the present time, these efforts havenot succeeded in producing clinically accurate results. Several systemshave used near-infrared spectroscopy and multivariate analysistechniques, but to date, no system for noninvasive measurement ofglucose using near-infrared spectroscopy appears to have gainedregulatory approval or appears to have been marketed in the U.S. Inaddition to multivariate and many other regression techniques, otherpractitioners have sought to extract a glucose signal from near-infraredtissue spectroscopy data using other methods of data reduction. Examplesof these include: subtractive techniques where the spectra ofinterfering substances are sequentially removed from a tissue spectrum,analysis of a number of equations with several unknowns, neuralnetworks, model trees, genetic algorithms, chaotic networks (and manyrelated approaches that can be classified as fast learning algorithms),and an optical method known as Kromoscopy (Appl. Opt. 2000 Sep. 1:39(25):4715-20). Many other approaches to measuring glucose in tissuehave also been attempted, and a book has been written on the subject:The Pursuit of Noninvasive Glucose: “Hunting the Deceitful Turkey” byJohn L. Smith, 4^(th) Edition (Copyright 2015), the disclosure of whichis incorporated herein by reference in its entirety. Like themultivariate techniques described above, these techniques have notsucceeded in producing clinically accurate results for noninvasivemeasurement of glucose. A new inventive approach for the direct,noninvasive measurement of glucose in tissue, as well as other analytesof interest, is therefore required.

The term “collision” has been used in different fields and contexts. Forexample, in computer networking and telecommunications and during theexecution of various algorithms processing data, data-packet collisionsgenerally imply that two distinct pieces of data have the same hashvalue, checksum, fingerprint, or cryptographic digest. The hashingcollisions typically allocate the same memory location to different datavalues. In the computational problem of determining the intersection oftwo or more computer animated objects, as encountered in simulationsand/or video games, linear algebra and computational geometry methods(e.g., the axis-aligned bounding box method for an n-body collisiondescribed in Lin, Ming C (1993). “Efficient Collision Detection forAnimation and Robotics (thesis)”. University of California, Berkeley),collision analysis techniques may be used to determine whether twoanimated objects would or have collided and the time of impact, and forpost-collision trajectory estimation. Computational atomic physics,which introduced a class of stochastic algorithms, such as those used ingame theory, molecular dynamics, social simulations, and econometrics,is inspired by techniques used in particle-field simulations. Thesetechniques generally involve collisions of atomic and subatomicparticles (such as those described in Sigurgeirsson et al. (2001),“Algorithms for Particle-Field Simulations with Collisions”, Journal ofComputational Physics 172, 766-807) and algorithms used for calculatingpost-collision electron and positron scattering and excitation in atomsand ions, such as in non-perturbative close coupling approach.

Various methods inspired by the classical Boltzmann collision operatorused in statistical physics or fluid simulations for describing theinteraction between colliding particles in rarefied gas includeBobylev-Rjasanow's Integral Transform Method, Pareschi-Russo's SpectralMethod, and Mouhot-Pareschi's method. These computational techniquestypically exploit the fundamental properties of the Boltzmann binarycollision operator (e.g., the Bhatnagar-Gross-Krook (BGK) operatordescribed in P. L. Bhatnagar, E. P. Gross, M. Krook (1954). “A Model forCollision Processes in Gases. I. Small Amplitude Processes in Chargedand Neutral One-Component Systems,” Physical Review 94 (3): 511-525)that are related to conservation of mass, momentum, and energy, to inferproperties of the colliding entities. While the binary collisionoperator and its approximation have been used in computer simulationsand modeling to infer properties of colliding entities, to date thesetechniques generally do not take into consideration the environment ofthe entities, such as noise, clutter from confounders, and ultra-weakmagnitudes of signals associated with entities of interest.

Computational collision techniques, such as those described inCollision-Based Computing, Andrew Adamatzky, (Ed.), ISBN978-1-4471-0129-1, generally appear to describe computer implementationsof various collisions described above, such collisions between particlesor collisions between physical entities. With reference to FIGS. 6-8B,collisions between two traveling waveforms can occur on a space-timegrid or a grid in another Cartesian coordinate system. In general, thetwo traveling waveforms move toward each other along a straight lineconnecting their centers of mass, with each point of one discretizedwavefront (102 in FIG. 6) engaging in a series of collision steps with acorresponding point of the other discretized waveform (104 in FIG. 6),with the result of each step being determined by a set of rulesestablished at the line of collision L_(C) (100 in FIG. 6). Those rulesdetermine the mathematical result of collision interactions and theshape of the resulting symbolic waveforms. Following completion of thesepartial steps in a collision between two waveforms, two resultingwaveforms (106, 108 in FIGS. 7A-7F) are typically produced. The tworesulting waveforms: (i) may be completely unchanged (except for a phaseshift or delay) relative to the colliding waveforms, as shown in FIG.7F), (ii) may be deformed (as shown in FIG. 8A), or (iv) either or bothwaveforms may be essentially completely destroyed (as shown in FIG. 8B).The nature of change in each waveform as a result of the collision(which can also be described as the degree of “elasticity” of thecollision) generally depends on the composition of the waveforms, therelative energy of each waveform, and the rules established at thecollision line L_(c). A “soliton” is an example of a waveform that doesdo not change its properties other than a delay or phase shift duringthe collision process.

SUMMARY

In various embodiments, the systems and methods described hereinfacilitate detection and/or measurement of the presence andconcentration of one or more chemical constituents of interest(generally called analytes) in a specified environment or a medium to beanalyzed (e.g., turbid layers of human tissue with inhomogeneities thatscatter light in random directions) in the presence of one or moreconfounders. This is achieved in part by employing one or morenonlinear, non-invertible computational collisions between twoentities—waveforms derived from sample observations, where the samplesare represented in an observation domain (also called a data-collectiondomain), and a purposefully constructed waveform that is typically notbased on the data-collection domain—yielding waveforms that can beprocessed to detect analyte presence and/or measure analyteconcentration in the uncharacterized samples. Various embodimentsdescribed herein provide for precise and accurate detection and/ormeasurement of an analyte of interest in a medium to be analyzed.Various embodiments also facilitate detection and/or measurement ofevents in different types of environments.

Specifically, in certain embodiments a new computational collisiontechnique is described whereby the presence and/or concentration ofclinical and chemical analytes can be determined from sensor data in thepresence of high noise, background interference, and interference fromother substances with similar properties as that of the analyte(s). Thiscomputational collision process can be extended to other types of datawhere the information sought is considered or treated as the equivalentof an analyte. Thus, detection and/or measurement of an analyte, asdescribed herein, may include the identification, characterization,and/or measurement of any material, property, magnitude, condition,anomaly, or an event of interest. The domain from which the source datafor the uncharacterized samples may originate is generally referred toas the data-collection domain.

Although collisions actually occur only within a computer, with theinteraction of what are termed “frequency components,” of two waveformsin the frequency domain, the collision process can be symbolicallydepicted as the collision between two discretized waveforms in asynthetic domain termed a “collision time domain.” For completeness andclarity, that process is described below in detail and illustrated inthe referenced figures.

When the waveforms to be collided are properly constructed and are madeco-dependent (as described below), energy changes (e.g., changes inspectral energy due to absorption of NIR radiation by the analytemolecules in a medium in certain embodiments) as derived from datacorresponding to particular materials, conditions, or events, can betransferred from one waveform to the other, and amplified in successivecollisions. In various embodiments, collision computing in which twoco-dependent waveforms collide, allows for drawing inferences about theunderlying properties of waveforms participating in the collision, basedon the energy transfer from one waveform to the other, and the energyproperties of the surviving waveform. In various embodiments, collisioncomputing facilitates an estimation of a Net Analyte Signal (NAS) fromspectral or other data sources. Through a projection process, the NAScan be used to determine the presence and/or the concentration of ananalyte in a medium to be analyzed.

Thus, in various embodiments, methods and systems described hereinprovide for detecting the presence of and for estimating concentrationof analytes from sensor data, by transforming the incoming sensor datato a waveform (Ψ_(CF)), i.e., a mathematical representation of thesensor data in the computer memory; colliding it with another waveformin the computer memory, referred to as the Zyoton (Ψ_(Z)), which isunrelated to and independent of the data domain of the sensor; andassessing the properties of the spectral energy of a modified Zyoton(Ψ_(Z′)) generated after the collision. Depending on the nature of inputdata, characteristics of the sensor used for observing the analyte,complexity and concentration of confounders, and expected concentrationof the analyte, one or more iterations of computational collisions maybe performed. After each collision operation between the two waveforms,the power spectral density of the collision-modified Zyoton Ψ_(Z′) isestimated. Waveform collisions may be implemented in the analog ordigital computing domain and in a time or frequency domain, i.e., thecolliding waveforms may be expressed in the time domain or in thefrequency domain. Analyte presence and concentration can be determinedbased on net gain or loss in the spectral energy after a selected numberof collision iterations. Observability of consistent patterns inspectral energy gain or loss after each collision between the twowaveforms is a prerequisite in various embodiments to concluding theintegrity and consistency of the collision process. The processing unitin which the collisions are implemented is denoted as the collisioncomputer.

Throughout this specification, data features which have been modified orconditioned by modulation (called conditioned features), as well as theZyotons, are described as waveforms. When these waveforms collide, thecollision operation takes place specifically at their wavefronts and, inthat context, these waveforms may be described as wavefronts. These twoterms are generally used separately to emphasize the special aspects ofthe collision computing process. Additionally, components of theoriginal data that interfere with the determination of the analyte orobscure its signal are referred to as confounders and, taken as a group,are represented by the term “clutter.” The collision computing processgenerally functions to improve the signal to clutter ratio by decreasingthe impact of the confounders present in the original data.

Unlike a collision between physical particles, which can be perfectly orimperfectly elastic or inelastic depending on how the kinetic energy andmomentum are conserved and whether the two particles continue to existas two entities, and unlike a collision between two waveforms that arenot specifically constructed to be co-dependent (as described below),the waveform collisions between two co-dependent waveforms describedherein are interferometric, where the two distinct but co-dependentwaveforms combine post-collision and the interaction is dissipative,that is, the spectral energy of the combined system is less than thepre-collision energies of two waveforms. Also, as a result of thiscollision, the two waveforms combine to a single waveform, called themodified Zyoton. The purposeful dissipation during collisions is causalin character and serves as a probe to characterize analytes of interestbecause, as described below, generally the energy associated with theanalyte of interest is transferred into the modified Zyoton while theenergy associated with noise and clutter may be discarded. Preciselymeasuring a change in the energy of the modified Zyoton relative to theenergy of the original Zyoton, in spectral regions (e.g., wavelengthranges) where the energy changes are most visible, allows us to quantifyconcentration of analytes with accuracy and reliability. As a designprinciple, the two waveforms and collision operators are designed basedon analysis of sensor data to intentionally maximize changes in spectralenergy in the spectral regions associated with the analyte, in eachcollision iteration. Also, the two waveforms are designed such that theZyoton waveform typically has higher initial spectral energy than theother waveform with which it collides.

One important aspect of various methods and systems described herein isthe discovery that very small portions of data (also called spectraldata features) contain analyte-specific frequency components thatpersist, even in the presence of overwhelming amounts of clutter, andthat these frequency components can be amplified and separated from thatclutter. As used herein the term “frequency components” generally refersto spatial frequencies, i.e., those components of a traveling waveformthat are periodic across position in space. These frequency components(or components) can be determined by a Fourier transform of atime-domain representation of the waveform.

Collision computing described herein facilitates the amplification andseparation of data. To this end, a stable waveform called a Zyoton,which generally does not change its shape and morphology when itpropagates through a propagation medium, is computationally collidedwith another waveform called a conditioned feature derived from aspectrum to be analyzed. The nature of the Zyoton and how it changesthrough the collision computing process are explained in detail below. Aconditioned feature is obtained by modulating a pre-selected, fixedcarrier waveform referred to as a carrier kernel having particularspectral properties, with the feature data to be analyzed. Inparticular, the spectral properties of the Zyoton and the carrier kernelare selected such that the Zyoton and the conditioned feature areco-dependent and can extract and amplify, in substance, the energyassociated with the analyte but not with the noise and/or clutter. Thus,post-collision, the modified Zyoton waveform may represent,substantially, the energy loss in the radiation energy incident upon themedium due to the absorption of such energy by the analyte of interest,if present in the medium, or the presence of one or more confounders inthe medium, or both, as well as, optionally, the radiant energy lost todissipative processes such as scattering, specifically in the spectralregion chosen for the feature.

Optionally, collision computing can be applied to analyze andcharacterize analyte presence or concentration from the emission spectraof a medium, which includes the spectrum of frequencies ofelectromagnetic radiation emitted due to an atom or molecule making atransition from a high energy state to a lower energy state. The energyof the emitted photon is equal to the energy difference between the twostates. The energy states of the transitions can lead to emissions overa range of frequencies yielding an emission spectrum. By observing thefrequencies and amplitudes of wavelengths in an emission spectrum, e.g.,as spectral energy or changes therein at different wavelength ranges,elemental or molecular composition of the sample or concentration of ananalyte in complex samples can be determined.

Example sources of emitted light are described in the table below:

TABLE 1 Name Source Example Chemiluminescence Chemical Glow sticksreactions Triboluminescence Friction energy Light emission seen whenpulling friction tape off the roll in the dark. BioluminescenceBiological Light emission seen from processes fireflies and somejellyfish Thermoluminescence Heat energy Used for archeological datingElectroluminescence Electric voltage Source of light seen in LEDsFluorescence Light energy Immediate re-emission after absorption oflight Phosphoresence Light energy Delayed re-emission after absorptionof light Blackbody emission All materials Red-hot metal; the human above0° K body at 300° K

Collision computing treatment of spectra acquired in absorptionspectroscopy or emission spectroscopy can be performed similarly asdescribed above, to the extent of extracting spectral features fromdifferent wavelength regions, conditioning them using carrier kernelwaveforms as described below, colliding them with Zyotons to estimatethe absorbed or emitted energy change, and then transforming that resultto conclude the presence of and/or to estimate the amount of theanalyte. In part due to the shape and morphology preservation propertiesof the Zyoton, the collision produces a resulting waveform that canrepresent a change in energy substantially related only to the energyloss represented by the feature used in the collision, and not due tothe collision operation itself. Moreover, the collision operator and oneor more parameters thereof are selected such that the energy changerepresented by the feature is amplified when that change is representedin the resulting waveform. The resulting waveform (the modified Zyoton)can be collided iteratively with the same or different Zyotons, in orderto further amplify the energy loss represented by the feature, withoutsubstantially introducing any noise or distortion.

Beyond the difficult problem of noninvasive glucose measurementdescribed above, which is generally considered intractable using variousknown techniques, there are many other measurements of high value thatcannot be performed affordably or reliably using various knownanalytical techniques and sensors, typically due to any of: lack ofdirect, unique markers or sensor signatures; an ultra-weak detectedsignal; overwhelming amount of interference or clutter that may obscurethe signal of interest (where clutter can be described as othermaterials or sources of noise which may interfere with the signal in thedata-collection domain. For example, in measurement of glucose intissue, other materials in tissue that absorb in the same spectralregion as the analyte, e.g., glucose, or the noise generated by thescattering of light by tissue, are generally considered to be clutter.Materials which absorb radiation in the same spectral region as theanalyte are often referred to as confounders); rapidly changingbackground or tissue medium properties; inadequate or narrow measurementtime window; or a combination of two or more of these exacerbatingfactors.

Nonlimiting examples of these measurement problems in various domainssuitable for analysis with collision computing include:

-   -   a. Concentration measurements of biologically important        molecules, either in-vivo or in-vitro, that have a cross-product        of concentration and measurable property (absorbance, emission,        fluorescence, magnetic cross-section, etc.) that is below the        measurement limit of various known measurement systems;    -   b. Measurement of environmental toxins at concentrations below        an existing detection threshold;    -   c. Accurate heart-rate and metabolic state tracking during        exercise and variable motion using photoplethysmograph (PPG)        devices;    -   d. In-vivo, early detection and continuous monitoring near-skin        and deep tissue inflammation or infection e.g., detection and        monitoring post-surgery, post stem-cell therapy, etc.;    -   e. Direct detection of circulating tumor cells using        nanoparticle tagging;    -   f. Isolation and real-time detection of sophisticated        cyberthreats including cyber-theft and injection of dormant,        cyber viruses that can dramatically compromise privacy,        information security, and infrastructure security;    -   g. Real-time steganography detection in video, audio, and        digital imagery;    -   h. Remote identification of subsurface mineral, oil, gas, or        water resources from the ground, aircraft or spacecraft,        including water-table depletion mapping; and    -   i. The location, mapping, and characterizing of underground        activities in hidden facilities.

Accordingly, in one aspect, a method is provided for determiningconcentration of glucose in a tissue sample. The method may includeobtaining energy absorbed by glucose from energy directed to the tissuesample, as a result of a collision between two co-dependent waveforms,and projecting the energy absorbed by glucose to a glucoseconcentration.

In various embodiments, the method may include: receiving a featurecorresponding to a specified wavelength range of a spectral signal,where the spectral signal generally represents at least one of: (i)absorption of energy, within the specified wavelength range, and (ii)loss of energy within the specified wavelength range due to scattering.Glucose in the tissue sample, and/or one or more confounders in thetissue may absorb the energy that is represented by the receivedfeature. The method may also include generating a conditioned feature bymodulating a carrier kernel using the received feature.

The step of receiving the feature may include directing near-infraredradiation to the tissue sample, collecting radiation from the tissuesample, generating an absorption spectrum from the collected radiation,and selecting a region of the absorption spectrum bounded by thewavelength range as the feature. Collecting the radiation may includereceiving diffusely reflected radiation from the tissue sample and/orreceiving radiation transmitted through the tissue sample. In someinstances, one of the two co-dependent waveforms comprises an originalZyoton constructed to amplify energy absorbed by the feature, and thecarrier kernel is constructed such that the original Zyoton and theconditioned feature obtained by modulating the carrier kernel using thefeature are co-dependent. The step of colliding the original Zyoton withthe conditioned feature may include, in a first iteration, colliding theoriginal Zyoton with the conditioned feature to obtain a modifiedZyoton, and renormalizing the modified Zyoton to obtain a renormalizedZyoton.

In various embodiments, the method also includes: in each of

−1 additional iterations, where

>1, colliding the original Zyoton with a renormalized Zyoton from animmediately preceding iteration, to obtain a remodified Zyoton, andrenormalizing the remodified Zyoton to obtain a renormalized modifiedZyoton. The method may further include computing energy gain of therenormalized modified Zyoton obtained after

iterations relative to energy of the original Zyoton, to determine theenergy absorbed by glucose. In some cases, the number of iterations

is selected such that accuracy of the glucose concentration measurement,as determined by Absolute Relative Deviation (ARD) relative to a glucoseconcentration measurement obtained using a reference method, is lessthan 15%.

In other cases, the number of iterations

is selected such that accuracy of a plurality of glucose concentrationmeasurements, as determined by Mean Absolute Relative Deviation (MARD)relative to a plurality of glucose concentration measurements obtainedusing a reference method, is less than 15%. The conditioned feature maybe derived from a glucose feature, where the glucose feature representsat least absorption of energy by glucose within a first specifiedwavelength range.

In various embodiments, the method includes: repeating the steps (a)through (c) with respect to another conditioned feature derived from anon-glucose feature paired with the glucose feature, forming a firstfeature pair. The non-glucose feature may represent absorption ofenergy, within a second specified wavelength range, by at least oneconfounder in the tissue sample. Alternatively or in addition, thenon-glucose feature may represent loss of energy due to scatteringwithin the second specified wavelength range. The method may furtherinclude: computing energy gain of the renormalized modified Zyotoncorresponding to the non-glucose feature relative to energy of theoriginal Zyoton, and computing net renormalized spectral energy gain(NRSEG) for the first feature pair based on energy gains correspondingto the glucose feature and the non-glucose feature of the first featurepair.

The method may also include normalizing the NRSEG for the first featurepair according to a weight designated to the first feature pair, toobtain a normalized NRSEG. In some instances, receiving the glucosefeature and the non-glucose feature may include directing, via a source,near infra-red radiation to the tissue sample, and collecting, via adetector, radiation from the tissue sample. In various embodiments, theprojecting step may include: (i) computing a number of NRSEG values forthe first feature pair, where each NRSEG value corresponds to arespective illumination state of the near infra-red radiation from anillumination sequence. In general, different illumination states cantarget light paths of different lengths and/or at different depthsthrough the tissue sample.

The method may further include (ii) computing a normalized absorptiongradient (NAG) based on the several NRSEG values; and (iii) selectingfrom a number of individual projector curves one particular individualprojector such that the computed NAG is within lower bound and upperbound NAG values associated with that individual projector curve. Themethod may also include (iv) determining glucose concentration using theselected individual projector curve and a representative energyabsorption value based on a plurality of energy absorption values.

In certain embodiments, the method further includes repeating step (i)described above for each additional feature pair in a set of featurepairs that includes the first feature pair, and computing a number ofNRSEG values for each additional feature pair in the set. Each NRSEGvalue of the various NRSEG values associated with a particular featuremay correspond to a respective illumination state of the near infra-redradiation from an illumination sequence. The computing the NAG mayinclude: for each feature pair in the set designated as acceptable: (A)computing an absorption gradient (AG), and (B) weighting the AGaccording to a weight associated with the corresponding acceptablefeature pair. Computing the NAG may also include averaging the weightedAGs. The representative energy absorption value can be computed by:selecting a particular illumination state; for each feature pair in theset designated as acceptable, weighting an NRSEG value corresponding tothe particular illumination state according to a weight associated withthe corresponding acceptable feature pair; and averaging the weightedNRSEG values. The representative energy absorption value may then be setto the average of the weighted NRSEG values. In general, a set includesat least one member.

In various embodiments, the method includes, prior to computing the NAG,for the several NRSEG values corresponding to at least one feature pairin the set, computing a mean NRSEG value, and excluding an NRSEG valuethat is different from the mean NRSEG value by a specified threshold.The method may also include determining monotonicity of the plurality ofNRSEG values corresponding to each feature pair in the set, anddesignating each feature pair having monotonicity as acceptable.

In some cases, determining the glucose concentration using the selectedindividual projector curve includes interpolation, which can includeadding to a product of the representative energy absorption value and aslope of the selected individual projector curve, an intercept of theselected individual projector curve. In some cases, determining thenormalized absorption gradient includes determining a slope of aregression of the plurality of NRSEG values, typically but notnecessarily normalized, with respect to the illumination states, theillumination states being ordered such that successive illuminationstates represent monotonically changing distance between the source andat least one detector. In some cases, projecting the energy absorbed byglucose to glucose concentration includes mapping the computed NRSEGvalue to glucose concentration using a single projector curve. Themethod may also include designating the determined glucose concentrationto one of a number of concentration bands. In certain instances,obtaining energy absorbed by glucose as a result of collision includes asingle collision iteration. Monotonically changing distance can bemonotonically increasing distance or monotonically decreasing distance.

In another aspect, a system is provided for determining concentration ofglucose in a tissue sample. The system may include a first processor anda first memory in electrical communication with the first processor, thefirst memory including instructions which, when executed by a processingunit including at least one of the first processor and a secondprocessor, and in electronic communication with a memory modulecomprising at least one of the first memory and a second memory, programthe processing unit to: obtain energy absorbed by glucose from energydirected to the tissue sample as a result of collision between twoco-dependent waveforms, and project the energy absorbed by glucose to aglucose concentration. In various embodiments, the instructions canprogram the processing unit to perform one or more of the method stepsdescribed above.

In another aspect, an article of manufacture is provided that includes anon-transitory storage medium having stored therein instructions which,when executed by a processing unit program the processing unit, which isin electronic communication with a memory module, to determineconcentration of glucose in a tissue sample. The instructions mayprogram the processing unit to: obtain energy absorbed by glucose fromenergy directed to the tissue sample as a result of collision betweentwo co-dependent waveforms, and project the energy absorbed by glucoseto a glucose concentration. In various embodiments, the instructions canprogram the processing unit to perform one or more of the method stepsdescribed above.

Performing Collision Computing

In another aspect, a method is provided for measuring a propertyassociated with an information signal. The method may include collidingusing a collision grid a first conditioned feature waveform that atleast partially represents a property of the information signal with anoriginal Zyoton, which includes a waveform that without a collisiontravels substantially unperturbed at a selected velocity in asubstantially constant propagation medium at least over a length of aspace-time grid, to obtain a first modified Zyoton, the firstconditioned feature waveform and the original Zyoton being constructedto: (i) be co-dependent, and (ii) transfer the property of theinformation signal to the first modified Zyoton through the collision.

In various embodiments, the space-time grid includes at least onespatial dimension and a time dimension. The information signal mayinclude one of a signal obtained from a sensor and a signal generated bydata analysis. In some instances, the method further includes derivingthe first conditioned feature waveform by modulating a carrier kernelusing a first feature derived from the information signal. In somecases, the method includes generating the first feature by: selectingfrom the information signal one of: (i) a single contiguous range ofwavelengths, and (ii) a combination of a plurality of discontiguousranges of wavelengths.

In other cases, the method includes generating the first feature by:transforming the information signal into a spectral signal; andselecting from the spectral signal one of: (a) a single contiguous rangeof wavelengths, and (b) a combination of a plurality of discontiguousranges of wavelengths. In some instances, modulating the carrier kernelincludes frequency modulation of the carrier kernel using the firstfeature. In other instances, modulating the carrier kernel includes:generating an intermediate signal by modulating the first feature usinga modulation signal; and modulating the carrier kernel with theintermediate signal. In other instances, modulating the carrier kernelincludes interpolating the first feature to match a length of theinterpolated first feature in time domain to a length of the carrierkernel in the time domain. In certain embodiments, constructing theoriginal Zyoton and the first conditioned feature waveform to beco-dependent includes determining whether an absolute difference betweena scaled velocity of the original Zyoton and a velocity of the firstconditioned feature does not exceed a threshold κ_(DV2).

In various embodiments, the method further includes adjusting at leastone of: (i) the velocity of the original Zyoton, and (ii) the velocityof the first conditioned feature waveform, such that the absolutedifference between the scaled velocity of the original Zyoton and thevelocity of the first conditioned feature is within the thresholdκ_(DV2). In some instances, the original Zyoton includes ananalyte-information-representing first group of frequency components anda non-analyte-information-representing group of frequency components,the first conditioned feature including corresponding groups offrequency components, the method further including: adjusting using ascaling vector at least one of: (i) a frequency domain amplitude of atleast one component of the analyte-information-representing group of theoriginal Zyoton, and (ii) a frequency domain amplitude of at least onecomponent of the corresponding group of the first conditioned featurewaveform, such that the absolute difference between the scaled velocityof the original Zyoton and the velocity of the first conditioned featureis within the threshold κ_(DV2).

The method may also include renormalizing the first modified Zyoton toobtain a first renormalized Zyoton. In certain cases, the property ofthe information signal includes energy absorbed by at least one of ananalyte and one or more confounders, the first renormalized Zyotonincludes a set of analyte-information-representing components and a setof non-analyte-information-representing components, and the set ofanalyte-information-representing components of the first renormalizedZyoton represents the energy absorbed by at least one of the analyte andthe confounder. Not all members of the set ofanalyte-information-representing components may represent analyteinformation, however. Similarly, one or more members of the set ofnon-analyte-information-representing components may represent analyteinformation.

The method may further include colliding using the collision grid thefirst renormalized Zyoton with the original Zyoton to obtain a secondmodified Zyoton, and renormalizing the second modified Zyoton to obtaina second renormalized Zyoton. The method may also include iterating thecolliding and renormalizing steps (

−2) times,

>2, each iteration being based on a renormalized Zyoton from animmediately preceding iteration, and producing a new renormalizedZyoton, until a final renormalized Zyoton is produced after (

−2) iterations. In certain cases, the at least partially representedproperty of the information signal includes energy absorbed by at leastone of an analyte and a confounder in a wavelength range associated witha first feature corresponding to the first conditioned feature waveform,the final renormalized Zyoton includes a set ofanalyte-information-representing components and a set ofnon-analyte-information-representing components, and the set ofanalyte-information-representing components of the final renormalizedZyoton represents the energy absorbed by at least one of an analyte anda confounder in the wavelength range associated with the first feature.

In various embodiments, the method may further include: colliding usingthe collision grid a second conditioned feature waveform that at leastpartially represents the property of the information signal with theoriginal Zyoton, to obtain a new first modified Zyoton, the secondconditioned feature waveform and the original Zyoton being constructedto: (i) be co-dependent, and (ii) transfer the property of theinformation signal to the new first modified Zyoton through thecollision; renormalizing the new first modified Zyoton to obtain a newfirst renormalized Zyoton; and iterating the colliding and renormalizingsteps (

−2) times,

>2, each iteration being based on a new renormalized Zyoton from animmediately preceding iteration, and producing another new renormalizedZyoton, until a new final renormalized Zyoton is produced after (

−2) iterations.

In such embodiments, the new final renormalized Zyoton includes a set ofanalyte-information-representing components and a set ofnon-analyte-information-representing components, and the set ofanalyte-information-representing components of the new finalrenormalized Zyoton represents the energy absorbed by at least one of ananalyte and a confounder in a wavelength range associated with a secondfeature corresponding to the second conditioned feature waveform. Themethod may also include determining

based on at least in part at least one of a specified signal-to-clutterratio (SCR), a specified signal-to-noise ratio (SNR), a targetprecision, a target sensitivity, a target accuracy, a target stability,and an expected dynamic range of an analyte in a medium to be analyzed.

Renormalization can include downscaling, using a scaling vector,frequency domain amplitudes of a set of frequency components in ananalyte-information-representing band of the first modified Zyoton toobtain the first renormalized Zyoton. The scaling vector can be aplurality of preset values, and can be determined according to frequencydomain amplitudes of a set of frequency components in ananalyte-information-representing band of the original Zyoton. In certainembodiments, renormalization includes truncating the first modifiedZyoton by removing at least one frequency component in anon-analyte-information-representing band of the first modified Zyotonto obtain the first renormalized Zyoton, and distributing energy of theat least one removed frequency component among a set of remainingfrequency components in at least one of anon-analyte-information-representing band and a transition band of thefirst renormalized Zyoton.

In various embodiments, the method further includes determining, priorto renormalizing, whether an absolute difference between a velocity ofthe original Zyoton and a velocity of the first modified Zyoton does notexceed a threshold κ_(DV3). In some instances, the method includesdetermining, prior to renormalizing, whether divergence of the firstmodified Zyoton does not exceed a threshold τ. In some instances, themethod includes determining, prior to renormalizing, whether energy ofthe first modified Zyoton is greater than energy of the original Zyoton.In some cases, the method includes determining, after renormalizing,whether an absolute difference between a scaled velocity of the originalZyoton and a velocity of the first renormalized Zyoton does not exceed athreshold κ_(DV1).

The property of the information signal may include at least one of: (i)a spectral energy absorbed by at least one of an analyte and one or moreconfounders, (ii) another property of at least one of the analyte andthe confounder, and (iii) an information measure. The information signalmay include a sensor signal. In some cases, the sensor signal mayinclude one of: an intensity spectrum signal and an absorbance spectrumsignal. In some cases, the sensor signal may include an emissionspectrum, where the emission can be fluorescence, phosphorescence,black-body emission, etc. In some cases, the sensor signal includes atleast one of a reflectance signal, and a transmission signal. In somecases, the sensor signal includes electromagnetic radiation receivedfrom a medium to be analyzed. The electromagnetic radiation may includenear infra-red radiation. The collision grid may include afrequency-domain grid, and colliding may involve a first bracketedconditional interaction, in frequency domain, between a first componentof the original Zyoton and a first bracket of components of the firstconditional feature waveform.

In various embodiments, the first bracketed conditional interaction mayinclude, for each component of the first conditional feature waveform inthe first bracket: testing if frequencies of the component of the firstconditioned feature waveform and the first component of the originalZyoton satisfy a first epsilon test; if the first epsilon test succeeds,generating a component of the first modified Zyoton, and setting anamplitude of the generated component of the first modified Zyoton as aproduct of amplitudes of the component of the first conditioned featurewaveform and the first component of the original Zyoton; if thefrequencies of the component of the first conditioned feature waveformand the first component of the original Zyoton satisfy a second epsilontest, setting a frequency of the generated component of the firstmodified Zyoton to a frequency of the first component of the originalZyoton; and otherwise setting the frequency of the generated componentof the first modified Zyoton to a sum of frequencies of the component ofthe first conditioned feature waveform and the first component of theoriginal Zyoton.

The first epsilon test may be selected based on to which group ofcomponents of the original Zyoton the first component of the originalZyoton belongs. In some cases, the first epsilon test is the secondepsilon test. In certain instances, colliding may involve a secondbracketed conditional interaction, in frequency domain, between a secondcomponent of the original Zyoton and a second bracket of components ofthe first conditional feature waveform. In such instances, the firstbracketed conditional interaction may produce a first component of themodified Zyoton and the second bracketed conditional interaction mayproduce a second component of the modified Zyoton, and the method mayfurther include: determining if the first and second modified Zyotoncomponents are to be merged by testing if frequencies of the first andsecond modified Zyoton components satisfy a third epsilon test. Thethird epsilon test can be selected based on to which group of componentsof the modified Zyoton a larger one of the first and second componentsof the modified Zyoton belongs, the larger component being determined bycomparing amplitudes of the first and second components of the modifiedZyoton.

In various embodiments, the method may further include merging the firstand second modified Zyoton components into the first modified Zyotoncomponent by resetting an amplitude of the first modified Zyotoncomponent to a sum of amplitudes of the first and second modified Zyotoncomponents, and removing the second modified Zyoton component. In somesuch embodiments, merging the first and second modified Zyotoncomponents into the first modified Zyoton component may further include,if a frequency of the first modified Zyoton component is smaller than afrequency of the second modified Zyoton component, setting a frequencyof the first modified Zyoton component to the frequency of the secondmodified Zyoton component.

In other such embodiments, merging the first and second modified Zyotoncomponents into the first modified Zyoton component may further include,if, prior to merging, the amplitude of the first modified Zyotoncomponent is smaller than the amplitude of the second modified Zyotoncomponent, setting a frequency of the first modified Zyoton component tothe frequency of the second modified Zyoton component. The method mayfurther include selecting a length of the first bracket of components ofthe first conditional feature waveform based at least in part on atleast one of a specified signal-to-clutter ratio (SCR), a specifiedsignal-to-noise ratio (SNR), a target precision, a target sensitivity, atarget accuracy, a system stability, and an expected dynamic range of ananalyte in a medium to be analyzed. The method may also include, priorto the first bracketed conditional interaction, at least one of: (i)shifting components of the original Zyoton according to a delay-shiftparameter, (ii) scaling an amplitude of the first component of theoriginal Zyoton according to at least one of (a) a precision of acomputing device, (b) a dynamic range of a computing device, (c) aresolution of a sensor used to obtain a feature used to generate thefirst conditioned feature, (d) a dynamic range of the sensor, and (e)SNR of the sensor, and (iii) applying a phase rotation to the firstcomponent of the original Zyoton.

In various embodiments, the original Zyoton includes a plurality ofcomponents selected from a kernel of components of a base Zyotongenerated from a family of waveforms, a number of components in theplurality being based on at least in part at least one of a specifiedsignal-to-clutter ratio (SCR), a specified signal-to-noise ratio (SNR),a target precision, a target sensitivity, a target accuracy, a targetstability, and an expected dynamic range of an analyte in a medium to beanalyzed. The collision grid may include a frequency-domain grid, and alength of the original Zyoton may include a sum of: (i) a number (k) ofanalyte-information-representing components, (ii) a number (m) oftransition components, and (iii) a number (j) ofnon-analyte-information-representing components of the original Zyoton.

In some embodiments, the original Zyoton is synthesized from at leastone of a plurality of waveform families comprising: solitons;autosolitons; similaritons; custom solitons generated using asine-Gordon-based equation; self-compressing similaritons;vortex-solitons; multi-color solitons; parabolic-similaritons; Riccisolitons; wavelets; curvelets; ridgelets; bions; elliptic wavescomprising at least one of Jacobi elliptic functions and Weierstrasselliptic functions; and nonautonomous similinear wave equation.

In other embodiments, the original Zyoton is synthesized from at leastone of a plurality of waveform generators comprising: meromorphicfunctions; Gamma functions; Riemann Zeta functions; regular instantons;Frobenius manifolds; harmonic oscillators; Hermite polynomials;polynomial sequences; asymptotic Hankel functions; Bessel functions;fractals; Neumann functions (spherical); poweroid coupled withsinusoidal functions; spatial random fields; cyclostationary series;random number generators; spherical harmonics; chaotic attractors;exponential attractors; multipoint Krylov-subspace projectors; Lyapunovfunctions; inertial manifolds of Navier-Stokes equation; evolutionequation for polynomial nonlinear reaction-diffusion equation; evolutionequation for Kuramoto-Savashinsky equation; evolution equation ofexponential attractors; Fourier series; and Ramanuj an theta functions.

In some cases, the original Zyoton is synthesized from a random numbergenerator having a replicability and at least one of: a periodicity ofat least 1000, a correlation between a pair of generated values of atmost 90%, and a spectral bandwidth of at least 100 Hz. In some cases,the original Zyoton is synthesized from a polynomial sequence, a Fouriertransform of the polynomial sequence having a spectral bandwidth of atleast 100 Hz. In certain instances, the original Zyoton is synthesizedfrom a random number generator comprising at least one of: a linearcongruential generator, a multiplicative congruential generator, anadditive congruential generator, and a Fibonacci generator. In certaininstances, the original Zyoton is synthesized from a polynomial sequencecomprising at least one of an Abel polynomial sequence and a Bellpolynomial sequence. In some embodiments, the original Zyoton issynthesized, at least in part, from at least one of: (i) a waveformfamily and (ii) a waveform generator, and the method further includes atleast one of transforming and reducing a function to at least one of thewaveform family and the waveform generator. In some cases, the originalZyoton is synthesized by at least one of: an addition, a multiplication,and a subtraction of at least two waveforms derived from at least twowaveform families.

In another aspect, a system is provided for measuring a propertyassociated with an information signal. The system may include a firstprocessor and a first memory in electrical communication with the firstprocessor, the first memory including instructions which, when executedby a processing unit including at least one of the first processor and asecond processor, and in electronic communication with a memory modulecomprising at least one of the first memory and a second memory, programthe processing unit to: collide using a collision grid a firstconditioned feature waveform that at least partially represents aproperty of the information signal with an original Zyoton, whichincludes a waveform that without a collision travels substantiallyunperturbed at a selected velocity in a substantially constantpropagation medium at least over a length of a space-time grid, toobtain a first modified Zyoton, the first conditioned feature waveformand the original Zyoton being constructed to: (i) be co-dependent, and(ii) transfer the property of the information signal to the firstmodified Zyoton through the collision. In various embodiments, theinstructions can program the processing unit to perform one or more ofthe method steps described above.

In another aspect, an article of manufacture is provided that includes anon-transitory storage medium having stored therein instructions which,when executed by a processing unit program the processing unit, which isin electronic communication with a memory module, to measure a propertyassociated with an information signal. The instructions may program theprocessing unit to: collide using a collision grid a first conditionedfeature waveform that at least partially represents a property of theinformation signal with an original Zyoton, which includes a waveformthat without a collision travels substantially unperturbed at a selectedvelocity in a substantially constant propagation medium at least over alength of a space-time grid, to obtain a first modified Zyoton, thefirst conditioned feature waveform and the original Zyoton beingconstructed to: (i) be co-dependent, and (ii) transfer the property ofthe information signal to the first modified Zyoton through thecollision. In various embodiments, the instructions can program theprocessing unit to perform one or more of the method steps describedabove.

Zyoton and Carrier Kernel Synthesis

In another aspect, a method is provided for enabling extraction of aproperty of an element of a specified environment. The method mayinclude selecting using at least one of: (i) at least one waveformfamily, and (ii) at least one waveform generator, a set of frequencycomponents for an analyte-information-representing band and a set offrequency components for a non-analyte-information-representing band;and synthesizing a Zyoton by combining the set of frequency componentsselected for the analyte-information-representing band and the set offrequency components selected for the non-analyte-informationrepresenting band, where: at least one frequency component in the set offrequency components for the analyte-information-representing bandcorresponds to a property to be extracted; at least one of the frequencycomponents for the non-analyte-information representing band does notcorrespond significantly to the property to be extracted; and theselected set of frequency components of the waveform family allow theZyoton to propagate through a substantially constant propagation mediumover a length of a collision grid without substantial change inmorphology thereof. Not all members of the band ofanalyte-information-representing components may represent analyteinformation, however. Similarly, one or more members of the band ofnon-analyte-information-representing components may represent analyteinformation.

In some embodiments, after a collision of the Zyoton with a waveformconstructed to perturb the Zyoton within specified limits, the selectedset of frequency components allow: generation of a modified Zyoton viathe collision; and subsequent propagation of the modified Zyoton throughthe substantially constant propagation medium over the length of thecollision grid without substantial change in morphology of the modifiedZyoton. In some cases, the at least one waveform family may include atleast one of: optical solitons, autosolitons, similaritons, customsolitons generated using a sine-Gordon-based equation, self-compressingsimilaritons, vortex-solitons, multi-color solitons,parabolic-Similaritons, and Ricci solitons.

In some cases, the at least one waveform family includes at least oneof: solitons; wavelets; curvelets; ridgelets; bions; elliptic wavescomprising at least one of Jacobi elliptic functions and Weierstrasselliptic functions; and nonautonomous similinear wave equations. In somecases, the at least one waveform generator includes at least one of:meromorphic functions; Gamma functions; Riemann Zeta functions; regularinstantons; Frobenius manifolds; harmonic oscillators; Hermitepolynomials; polynomial sequences; asymptotic Hankel functions; Besselfunctions; fractals; Neumann functions (spherical); poweroid coupledwith sinusoidal functions; spatial random fields; cyclostationaryseries; random number generators; spherical harmonics; chaoticattractors; exponential attractors; multipoint Krylov-sub spaceprojectors; Lyapunov functions; inertial manifolds of Navier-Stokesequation; evolution equation for polynomial nonlinear reaction-diffusionequation; evolution equation for Kuramoto-Savashinsky equation;evolution equation of exponential attractors; Fourier series; andRamanuj an theta functions.

In certain instances, the specified environment includes a medium to beanalyzed; and the property to be extracted includes at least one of:presence of an analyte, absence of the analyte, a quantity of ananalyte, and a rate of change of the quantity of the analyte, in themedium to be analyzed. In various embodiments, the method may furtherinclude selecting from the at least one waveform family a set offrequency components for a transition band, and synthesizing the Zyotonby combining the set of frequency components for theanalyte-information-representing band, the set of frequency componentsfor the transition band, and the set of frequency components for thenon-analyte-information-representing band.

In another aspect, a system is provided for enabling extraction of aproperty of an element of a specified environment. The system mayinclude a first processor and a first memory in electrical communicationwith the first processor, the first memory including instructions which,when executed by a processing unit including at least one of the firstprocessor and a second processor, and in electronic communication with amemory module comprising at least one of the first memory and a secondmemory, program the processing unit to: select using at least one of:(i) at least one waveform family, and (ii) at least one waveformgenerator, a set of frequency components for ananalyte-information-representing band and a set of frequency componentsfor a non-analyte-information representing band; and synthesize a Zyotonby combining the set of frequency components selected for theanalyte-information-representing band and the set of frequencycomponents selected for the non-analyte-information-representing band.

At least one frequency component in the set of frequency components forthe analyte-information-representing band corresponds to a property tobe extracted; at least one of the frequency components for thenon-analyte-information-representing band does not correspondsignificantly to the property to be extracted; and the selected set offrequency components of the waveform family allow the Zyoton topropagate through a substantially constant propagation medium over alength of a collision grid without substantial change in morphologythereof. In various embodiments, the instructions can program theprocessing unit to perform one or more of the method steps describedabove.

In another aspect, an article of manufacture is provided that includes anon-transitory storage medium having stored therein instructions which,when executed by a processing unit program the processing unit, which isin electronic communication with a memory module, to enable extractionof a property of an element of a specified environment. The instructionsmay program the processing unit to: select using at least one of: (i) atleast one waveform family, and (ii) at least one waveform generator, aset of frequency components for an analyte-information-representing bandand a set of frequency components for a non-analyte-informationrepresenting band; and synthesize a Zyoton by combining the set offrequency components selected for the analyte-information-representingband and the set of frequency components selected for thenon-analyte-information-representing band.

At least one frequency component in the set of frequency components forthe analyte-information-representing band corresponds to a property tobe extracted; at least one of the frequency components for thenon-analyte-information-representing band does not correspondsignificantly to the property to be extracted; and the selected set offrequency components of the waveform family allow the Zyoton topropagate through a substantially constant propagation medium over alength of a collision grid without substantial change in morphologythereof. In various embodiments, the instructions can program theprocessing unit to perform one or more of the method steps describedabove.

In another aspect, another method is provided for enabling extraction ofa property of an element of a specified environment. The method mayinclude receiving a representative spectral signal from adata-collection domain, the representative spectral signal indicating aproperty of the element of the specified environment; generating aZyoton from at least one waveform family, the at least one waveformfamily being independent of the data-collection domain; and generating aco-dependent carrier kernel for conditioning at least one featurecorresponding to the representative spectral signal. In some instances,the element of the specified environment includes an analyte, and theproperty of the element of the specified environment includesconcentration of the analyte. In some cases, the specified environmentmay include at least one confounder.

In some cases, the specified environment may include a portion of skintissue, and the analyte may include glucose. In certain embodiments, theproperty of the element of the specified environment that is representedby the representative spectral signal includes energy loss via at leastone of: (i) absorption by the analyte, (ii) absorption by the at leastone confounder, (iii) noise generated by variation in absorption by theat least one confounder, and (iv) noise generated by scattering. The atleast one confounder may include a dominant confounder. Therepresentative signal may represent information about an analyte and/orone or more confounders.

In various embodiments, the representative signal includes a first modelsignal, and generating the Zyoton may include: obtaining a transformedsignal from the first model signal representing energy loss viaabsorption by the analyte; adding a noise signal to the transformedsignal to obtain a second signal; determining frequency components ofthe second signal; using the frequency components of the second signal,determining a number of frequency components required to separate a highanalyte absorption region of the transformed signal from a low analyteabsorption region of the transformed signal; selecting the at least onewaveform family according to a morphology of one of the first modelsignal, the transformed signal, and the second signal; obtaining a baseZyoton based on the at least one selected waveform family; and selectingthe determined required number of frequency components of the baseZyoton as frequency components of the Zyoton.

In some instances, the noise signal corresponds to an amount of noisethat is a multiple of at least one of: (i) a noise associated with thefirst model signal, and (ii) a noise associated with the transformedsignal; and the determined required number of frequency componentsrepresents a number of frequency components (k) required to separate thehigh analyte absorption region of the transformed signal from the lowanalyte absorption region of the transformed signal in presence of thespecified amount of noise. In some cases, obtaining the transformedsignal may include generating a second derivative of one of: the firstmodel signal and an interpolated first model signal.

In other cases, obtaining the transformed signal may include generatinga first composite signal by combining with the first model signal asecond model signal representing energy loss via absorption by at leastone non-dominant confounder, where the determined required number offrequency components represents a number of frequency components (m)required to separate the high analyte absorption region of thetransformed signal from the low analyte absorption region of thetransformed signal in presence of the at least one non-dominantconfounder.

In still other cases, obtaining the transformed signal may includegenerating a second composite signal by combining with the first modelsignal a third model signal representing energy loss via variations inabsorption by a dominant confounder; where the determined requirednumber of frequency components represents a number of frequencycomponents (j) required to separate the high analyte absorption regionof the transformed signal from the low analyte absorption region of thetransformed signal in presence of the dominant confounder and thespecified amount of noise.

The Zyoton may include k analyte-information-representing components,k≧1, and the method may further include: setting amplitudes of the kanalyte-information-representing components within a first range ofamplitudes according to an amplitude profile. The first model signal maycorrespond to a pure-component analyte signal, and the transformedsignal can be first, second, or higher-order derivative thereof.

In various embodiments, the method may further include generating theamplitude profile by: generating a plurality of wavelength-region pairs,each pair having a high absorption representing wavelength regioncorresponding to a respective wavelength range of the representativespectral signal and a low absorption representing wavelength regioncorresponding to a different respective wavelength range of therepresentative spectral signal; for each pair in the plurality ofwavelength-region pairs, computing a ratio of a magnitude of a region ofthe transformed signal corresponding to the high absorption representingwavelength region and a magnitude of a region of the transformed signalcorresponding to the low absorption representing wavelength region;determining a range of the magnitude ratios; and setting the amplitudeprofile as a function bounded by the range of magnitude ratios, thefunction being one of linear, quadratic, and exponential.

In some embodiments, the Zyoton includes kanalyte-information-representing components, k≧1, and jnon-analyte-information representing components, j≧1, the kanalyte-information-representing components having amplitudes within afirst range, and the method may further includes: randomly settingamplitudes of the j non-analyte-information representing componentswithin a second range of amplitudes, any amplitude in the second rangebeing less than 1/100 of any amplitude in the first range. In someinstances, the Zyoton further includes m transition components, m≧1, andthe method further includes: randomly setting amplitudes of the mtransition components within a third range of amplitudes, any amplitudein the third range being at least two times any amplitude in the secondrange.

Generating the co-dependent carrier kernel may include: for each of thek analyte-information-representing major components of the Zyoton,including in the carrier kernel as a correspondinganalyte-information-representing major component a frequency componenthaving a frequency within a specified threshold σ of frequency of thecorresponding analyte-information-representing k component of theZyoton; and including in the carrier kernel as at least one non-majorcomponent, at least one of: at least one harmonic of at least one of ananalyte-information-representing component, a transition component, andnon-analyte-information-representing component included in the carrierkernel; and for at least one non-major component of the Zyoton,including in the carrier kernel a frequency component having a frequencywithin the specified threshold σ of frequency of the correspondingnon-major component of the Zyoton.

In some instances, one of: the non-major component of the Zyoton is atransition component, and the corresponding non-major component of thecarrier kernel is a transition component; and the non-major component ofthe Zyoton is a non-analyte-information-representing j component, andthe corresponding non-major component of the carrier kernel is anon-analyte-information-representing j component. In certainembodiments, the method may further include setting amplitudes of theinformation-representing, transition, and non-information representingfrequency components of the carrier kernel according to the amplitudesof the respective analyte-information-representing, transition, andnon-analyte-information-representing Zyoton components scaled by apre-set scaling factor.

The method may also include: selecting an amplitude scaling coefficientsuch that: (i) a difference between a scaled velocity of the Zyoton,scaled by the amplitude scaling factor, and a velocity of the carrierkernel does not exceed a specified velocity difference thresholdκ^(SYN); and setting amplitudes of the analyte-information-representing,transition, and non-analyte-information-representing frequencycomponents of the carrier kernel according to the amplitudes of therespective analyte-information-representing, transition, andnon-analyte-information-representing Zyoton components scaled by theselected scaling factor.

In another aspect, another system is provided for enabling extraction ofa property of an element of a specified environment. The system mayinclude a first processor and a first memory in electrical communicationwith the first processor, the first memory including instructions which,when executed by a processing unit including at least one of the firstprocessor and a second processor, and in electronic communication with amemory module comprising at least one of the first memory and a secondmemory, program the processing unit to: receive a representativespectral signal from a data-collection domain, the representativespectral signal indicating a property of the element of the specifiedenvironment; generate a Zyoton from at least one waveform family, the atleast one waveform family being independent of the data-collectiondomain; and generate a co-dependent carrier kernel for conditioning atleast one feature corresponding to the representative spectral signal.In various embodiments, the instructions can program the processing unitto perform one or more of the method steps described above.

In another aspect, another article of manufacture is provided thatincludes a non-transitory storage medium having stored thereininstructions which, when executed by a processing unit program theprocessing unit, which is in electronic communication with a memorymodule, to enable extraction of a property of an element of a specifiedenvironment. The instructions may program the processing unit to:receive a representative spectral signal from a data-collection domain,the representative spectral signal indicating a property of the elementof the specified environment; generate a Zyoton from at least onewaveform family, the at least one waveform family being independent ofthe data-collection domain; and generate a co-dependent carrier kernelfor conditioning at least one feature corresponding to therepresentative spectral signal. In various embodiments, the instructionscan program the processing unit to perform one or more of the methodsteps described above.

Systems and Methods of Universal Projection

In another aspect, a method is provided for quantitating an analyte. Themethod may include: receiving from an uncharacterized sample an energychange value to be mapped, the energy change value corresponding to anuncharacterized sample; mapping the energy change value to be mapped toa quantity of an analyte in the uncharacterized sample, via anindividual projector curve associating: (i) energy change valuesobtained from a synthetic reference system to analyte quantities of thereference system, and (ii) energy change values obtained from anon-synthetic reference system to the analyte quantities of thereference system.

The method may further include: computing a representative absorptiongradient (AG) using a first set of energy change values corresponding toa first feature pair, each energy change value in the first setcorresponding to a respective path of radiation through a medium to beanalyzed; selecting the individual projector curve from a plurality ofprojector curves using the representative gradient value associated withthe first feature pair; and determining a quantity of an analyte usingthe selected individual projector curve, the energy change value to bemapped being a representative energy change value associated with thefirst feature pair.

The energy change value to be mapped can be a net renormalized spectralenergy gain, which may be optionally normalized. In some cases, therepresentative gradient value may include a normalized AG (NAG), and themethod further includes: weighting the representative gradientassociated with the first feature pair by a weight associated with thefirst feature pair, to obtain the NAG. Computing the representativeenergy change value can include weighting one energy change value fromthe first set of energy change values by a weight associated with thefirst feature pair. In certain instances, a plurality of feature pairsmay include the first feature pair, and the method may further include:generating a set of acceptable feature pairs from the plurality offeature pairs; for each feature pair in the set of acceptable featurepairs computing a respective absorption gradient (AG) using a respectiveset of energy change values corresponding to the feature pair; computingthe representative AG value as an average of the respective AGsassociated with each of the acceptable feature pairs. The energy valuechange can be a net, renormalized spectral energy gain corresponding toa feature or a feature pair, which may be optionally normalized.

In various embodiments, generating the set of acceptable feature pairsmay include testing for each feature pair in the plurality of featurepairs monotonicity of the corresponding set of energy change valuesacross a plurality of illumination states. Computing the AG for eachacceptable feature pair may include: determining a slope of a regressionof the corresponding set of energy change values with respect to theillumination states, the illumination states being ordered such thatsuccessive illumination states represent monotonically changing distancebetween the source and at least one detector.

Prior to computing the average, the method may further includenormalizing each of the AGs corresponding to the acceptable featurepairs using a weight associated with the corresponding acceptablefeature pair. In some cases, computing the representative energy changevalue includes: for each acceptable feature pair, selecting one energychange value from the respective set of energy change values; weightingfor each acceptable feature pair, the selected energy change value by aweight associated with the acceptable feature pair; and setting anaverage of the weighted energy change values as the representativeenergy change value. In some embodiments, the uncharacterized sampleincludes a portion of tissue; and the analyte includes glucose. In someembodiments, the energy change includes one of energy gain and energyloss.

In another aspect, a system is provided for quantitating an analyte. Thesystem may include a first processor and a first memory in electricalcommunication with the first processor, the first memory includinginstructions which, when executed by a processing unit including atleast one of the first processor and a second processor, and inelectronic communication with a memory module comprising at least one ofthe first memory and a second memory, program the processing unit to:receive an energy change value to be mapped, the energy change valuecorresponding to an uncharacterized sample; and map the energy changevalue to be mapped to a quantity of an analyte in the uncharacterizedsample, via an individual projector curve associating: (i) energy changevalues obtained from a synthetic reference system to analyte quantitiesof the reference system, and (ii) energy change values obtained from anon-synthetic reference system to the analyte quantities of thereference system. In various embodiments, the instructions can programthe processing unit to perform one or more of the method steps describedabove.

In another aspect, an article of manufacture is provided that includes anon-transitory storage medium having stored therein instructions which,when executed by a processing unit program the processing unit, which isin electronic communication with a memory module, to quantitate ananalyte. The instructions may program the processing unit to: receive anenergy change value to be mapped, the energy change value correspondingto an uncharacterized sample; and map the energy change value to bemapped to a quantity of an analyte in the uncharacterized sample, via anindividual projector curve associating: (i) energy change valuesobtained from a synthetic reference system to analyte quantities of thereference system, and (ii) energy change values obtained from anon-synthetic reference system to the analyte quantities of thereference system. In various embodiments, the instructions can programthe processing unit to perform one or more of the method steps describedabove.

System and Method of Generating a Projector Curve Set

In another aspect, a method is provided for calibrating a measurementsystem for non-invasive analyte measurement. The method may includeobtaining from a selected plurality of synthetic medium samples, eachhaving a reference analyte concentration, a plurality of energy-valuesets from the measurement system, each energy value in a particularenergy-value set corresponding to a respective reference analyteconcentration from the selected plurality of synthetic medium samples;generating a composite projector curve using the plurality of energyvalue sets and the plurality of reference analyte concentrations; andpartitioning the composite projector curve into a set of non-overlappingindividual projector curves according to a set of slopes of thecomposite projector curve, each individual projector curve beingidentified by a lower bound analyte concentration and an upper boundanalyte concentration. In some instances, the plurality of energy-valuesets includes a first energy-value set, each energy value in the firstenergy-value set corresponding to a first reference analyteconcentration, and the method may further include: excluding from thefirst energy-value set an energy value that is different from a mean ofthe energy values by a specified threshold.

In various embodiments, the method may further include obtaining fromrepresentative subjects a plurality of groups of energy value vectorsfrom the measurement system, each energy-value-vector groupcorresponding to a respective analyte concentration determined using areference invasive measurement system, and each energy-value vector in aparticular group corresponding to a respective feature pair;partitioning the plurality of groups of energy-value vectors into aplurality of projection sets, such that the analyte concentrationcorresponding to any energy-value-vector group in each projection set iswithin lower and upper bound analyte concentrations corresponding to asingle respective individual projector curve from the set of individualprojector curves; computing for each energy-value-vector group in eachprojection set, an average of normalized absorption gradients (NAGs),each NAG corresponding to an energy-value vector that corresponds to anacceptable feature pair; for each projector curve: designating as alower bound NAG a minimum of averaged NAGs of all energy-value-vectorgroups of the corresponding projection set; and designating as an upperbound NAG a maximum of averaged NAGs of all energy-value-vector groupsof the corresponding projection set. An energy-value vector may includea plurality of energy values, each energy value corresponding to anillumination state in an illumination sequence. In some instances, thepartitioning step may include rejecting from a group of energy-valuevectors any non-monotonic energy-value vector.

In another aspect, a system is provided for calibrating a measurementsystem for non-invasive analyte measurement. The system may include afirst processor and a first memory in electrical communication with thefirst processor, the first memory including instructions which, whenexecuted by a processing unit including at least one of the firstprocessor and a second processor, and in electronic communication with amemory module comprising at least one of the first memory and a secondmemory, program the processing unit to: obtain from a selected pluralityof synthetic medium samples, each having a reference analyteconcentration, a plurality of energy-value sets from the measurementsystem, each energy value in a particular energy-value set correspondingto a respective reference analyte concentration from the selectedplurality of synthetic medium samples.

The instructions may program the processing unit to generate a compositeprojector curve using the plurality of energy value sets and theplurality of reference analyte concentrations; and partition thecomposite projector curve into a set of non-overlapping individualprojector curves according to a set of slopes of the composite projectorcurve, each individual projector curve being identified by a lower boundanalyte concentration and an upper bound analyte concentration. Invarious embodiments, the instructions can program the processing unit toperform one or more of the method steps described above.

In another aspect, an article of manufacture is provided that includes anon-transitory storage medium having stored therein instructions which,when executed by a processing unit program the processing unit, which isin electronic communication with a memory module, to calibrate ameasurement system for non-invasive analyte measurement. Theinstructions may program the processing unit to: obtain from a selectedplurality of synthetic medium samples, each having a reference analyteconcentration, a plurality of energy-value sets from the measurementsystem, each energy value in a particular energy-value set correspondingto a respective reference analyte concentration from the selectedplurality of synthetic medium samples.

The instruction may program the processing unit to generate a compositeprojector curve using the plurality of energy value sets and theplurality of reference analyte concentrations; and partition thecomposite projector curve into a set of non-overlapping individualprojector curves according to a set of slopes of the composite projectorcurve, each individual projector curve being identified by a lower boundanalyte concentration and an upper bound analyte concentration. Invarious embodiments, the instructions can program the processing unit toperform one or more of the method steps described above.

In another aspect, a method is provided for computing analyteconcentration in a medium. The method may include: selecting a member ofa projector curve set according to a normalized absorption gradient(NAG) value, such that the NAG value is within a range of minimum andmaximum NAG values associated with that member; and interpolatinganalyte concentration using a slope and an intercept of the selectedmember. The method may further include: receiving for a feature pair, arespective net renormalized spectral energy gain (NRSEG) value for eachone of a plurality of illumination states; and designating the featurepair as acceptable feature pair, if the respective NRSEG values aremonotonic across the illumination states, and rejecting the featurepair, otherwise.

The method may also include: receiving for a first acceptable featurepair, a respective net renormalized spectral energy gain (NRSEG) valuefor each one of a plurality of illumination states; computing a firstabsorption gradient (AG), typically but not necessarily normalized,across the illumination states using the NRSEG values associated withthe first acceptable feature pair; and computing the NAG by applying tothe first AG a first weight corresponding to the first acceptablefeature pair. The method may also include: receiving for a secondacceptable feature pair, a respective net renormalized spectral energygain (NRSEG) value for each one of the plurality of illumination states;computing a second absorption gradient (AG) across the illuminationstates using the NRSEG values associated with the second acceptablefeature pair; and computing the NAG by applying to the second AG asecond weight corresponding to the second acceptable feature pair andaveraging the first and second weighted AGs.

In another aspect, a system is provided for computing analyteconcentration in a medium. The system may include a first processor anda first memory in electrical communication with the first processor, thefirst memory including instructions which, when executed by a processingunit including at least one of the first processor and a secondprocessor, and in electronic communication with a memory modulecomprising at least one of the first memory and a second memory, programthe processing unit to: select a member of a projector curve setaccording to a normalized absorption gradient (NAG) value, such that theNAG value is within a range of minimum and maximum NAG values associatedwith that member, and interpolate analyte concentration using a slopeand an intercept of the selected member. In various embodiments, theinstructions can program the processing unit to perform one or more ofthe method steps described above.

In another aspect, an article of manufacture is provided that includes anon-transitory storage medium having stored therein instructions which,when executed by a processing unit program the processing unit, which isin electronic communication with a memory module, to compute analyteconcentration in a medium. The instructions may program the processingunit to: select a member of a projector curve set according to anormalized absorption gradient (NAG) value, such that the NAG value iswithin a range of minimum and maximum NAG values associated with thatmember, and interpolate analyte concentration using a slope and anintercept of the selected member. In various embodiments, theinstructions can program the processing unit to perform one or more ofthe method steps described above.

PPG

In another aspect, a method is provided for generating features formeasurement of heart beats. The method may include receiving a signalbased on one of reflected and transmitted radiation from a tissue duringa global time interval starting at a global start time and ending at aglobal end time; designating a first portion of the signal starting atthe global start time and ending at a first end time less than theglobal end time as a first feature; designating a second portion of thesignal starting at the global start time and ending at a second end timegreater than the first end time as a second feature; and identifying astart of a heart-beat cycle within the first feature.

The method may further include determining that an expected end of theheart-beat cycle is absent within the first portion of the signal,designated as the first feature; and designating the first feature as anon-analyte feature. The method may also include determining that theexpected end of the heat-beat cycle is present within the second portionof the signal, designated as the second feature; and designating thesecond feature as an analyte feature. In certain embodiments, the methodmay include determining a heart rate by: colliding a first conditionedfeature waveform derived from the first feature with a co-dependentZyoton to obtain a first energy change; colliding a second conditionedfeature waveform derived from the second feature with a co-dependentZyoton to obtain a second energy change; computing an end of theheart-beat cycle using the first and second energy changes; andcomputing the heart-rate using the start of the heart-beat cycle and theend of the heart-beat cycle.

In another aspect, a system is provided for generating features formeasurement of heart beats. The system may include a first processor anda first memory in electrical communication with the first processor, thefirst memory including instructions which, when executed by a processingunit including at least one of the first processor and a secondprocessor, and in electronic communication with a memory modulecomprising at least one of the first memory and a second memory, programthe processing unit to: receive a signal based on one of reflected andtransmitted radiation from a tissue during a global time intervalstarting at a global start time and ending at a global end time;designate a first portion of the signal starting at the global starttime and ending at a first end time less than the global end time as afirst feature; designate a second portion of the signal starting at theglobal start time and ending at a second end time greater than the firstend time as a second feature; and identify a start of a heart-beat cyclewithin the first feature. In various embodiments, the instructions canprogram the processing unit to perform one or more of the method stepsdescribed above.

In another aspect, an article of manufacture is provided that includes anon-transitory storage medium having stored therein instructions which,when executed by a processing unit program the processing unit, which isin electronic communication with a memory module, to generate featuresfor measurement of heart beats. The instructions may program theprocessing unit to: receive a signal based on one of reflected andtransmitted radiation from a tissue during a global time intervalstarting at a global start time and ending at a global end time;designate a first portion of the signal starting at the global starttime and ending at a first end time less than the global end time as afirst feature; designate a second portion of the signal starting at theglobal start time and ending at a second end time greater than the firstend time as a second feature; and identify a start of a heart-beat cyclewithin the first feature. In various embodiments, the instructions canprogram the processing unit to perform one or more of the method stepsdescribed above.

BRIEF DESCRIPTION OF THE FIGURES

In the drawings, like reference characters generally refer to the sameparts throughout the different views. Also, the drawings are notnecessarily to scale, emphasis instead generally being placed uponillustrating the principles of the invention. In the followingdescription, various embodiments of the present invention are describedwith reference to the following drawings, in which:

FIG. 1 shows an example of a noninvasive near-infrared intensity(diffuse reflectance) spectrum of a tissue sample;

FIG. 2 shows an example tissue absorbance spectrum from a single samplewhich is used with other similar measurements and their associatedreference values to create a multivariate model for analyte measurement;

FIG. 3 shows an example set of regression coefficients versus wavelengthassociated with a model used in multivariate analysis for analytemeasurement;

FIG. 4 is a flow-chart depicting the use of a multivariate model topredict a tissue analyte;

FIG. 5 illustrates normalized absorbance spectra of various tissueconstituents with an overlaid tissue absorbance spectrum;

FIG. 6 shows two waveforms on a collision time grid as both approach thecollision line;

FIGS. 7A-E show two waveforms colliding on a collision time grid atvarious stages of the collision, with the resulting waveforms as thecollision process progresses;

FIG. 7F shows two waveforms such as solitons, which are unchanged aftercompleting the collision process;

FIGS. 8A-8B show the severe distortion or complete destruction of twonon-soliton waveforms after the collision process;

FIG. 9 shows the distribution of energy from two features;

FIG. 10A shows exemplary spectra for an analyte and two confounders;

FIG. 10B shows absorption components of a feature;

FIG. 10C shows frequency components from a conditioned feature;

FIG. 10D shows frequency components from an analyte and confounders;

FIG. 10E shows frequency components from an analyte and otherconfounders;

FIG. 11 shows frequency components for an modified Zyoton and arenormalized Zyoton;

FIGS. 12A and 12B show the morphological profile and amplitude envelopeof an example Zyoton waveform used in collision computing;

FIG. 12C shows the primary and sideband peaks of a Zyoton waveform;

FIG. 13 is a flowchart depicting an exemplary process for detectingand/or quantifying an analyte of interest in a medium, according to anexample embodiment;

FIGS. 14A-14B shows the dispersion of a Zyoton before and after acollision;

FIG. 15 depicts an exemplary process for determining one or moreoperating parameters of a collision computer and for generating theinputs thereof, according to one embodiment;

FIG. 16 is a flowchart depicting a process for renormalizing a modifiedZyoton prior to a subsequent collision, according to one embodiment;

FIG. 17 shows the conditioned feature waveform on the collision grid andZyoton waveform before a collision;

FIG. 18 shows the conditioned feature waveform on the collision grid andzyoton waveform at the beginning of a collision;

FIG. 19 shows successive views of the collision between a conditionedfeature waveform and Zyoton wavefronts during a collision;

FIG. 20 shows the modified Zyoton after a collision;

FIG. 21 shows the renormalized modified Zyoton after the collision andpreceding the next collision in a multi-collision protocol;

FIG. 22 shows the modified and normalized Zyoton after a finite numberof k collisions in a multi-collision protocol;

FIG. 23 shows how the normalized energy trajectory evolves for twofeatures drawn from samples with two different material concentrationsin a collision computer with the difference in the two waveforms showingthe amplification that results from a collision computer;

FIG. 24 shows a time-domain representation of a Zyoton and a conditionedfeature;

FIG. 25 shows a time-domain representation of a Zyoton after a singlecollision;

FIG. 26 shows a time-domain representation of a Zyoton and arenormalized modified Zyoton;

FIG. 27 shows a time-domain representation of the energy of a Zyotonafter a second collision;

FIGS. 28A and 28B show the pure component absorbance spectra for ananalyte of interest and a confounder: glucose and collagen,respectively;

FIGS. 29A and 29B show the first derivative of pure component absorbancespectra for the compounds shown in FIGS. 28A and 28B);

FIGS. 30A and 30B show the second derivative of pure componentabsorbance spectra for the compounds shown in FIGS. 28A and 28B);

FIG. 31A shows the near-infrared diffuse reflectance intensity as afunction of wavelength for human skin, and FIG. 31B shows the associatedabsorbance spectrum of human skin;

FIG. 32 provides an example of the absorbance spectrum of a singlefeature from a single illumination of tissue;

FIG. 33 provides an example of a set of mean-centered absorbance spectrato show instrument related spectral variability as a function of NIRwavelength;

FIG. 34 gives an example of a wavelength by wavelength RMS noiseestimate based upon a set of spectra;

FIG. 35 provides an example of a noise intensity spectrum in NIRwavelengths;

FIG. 36 shows the scaled intensity and absorbance spectra associatedwith a single feature, with scaled absorbance for glucose, fat, andwater confounders overlaid on the plot;

FIG. 37 depicts a process for conditioning a feature prior to collisionthereof with a collision waveform, according to one embodiment;

FIG. 38 is a flowchart showing the steps in the generation of a Zyotonand a carrier kernel waveform;

FIG. 39 is a flowchart showing the steps in the determination of thenumber k of the frequency components of a Zyoton and a carrier kernel,according to one embodiment;

FIG. 40 is a flowchart showing the steps in the determination of thenumber m of the frequency components of a Zyoton and a carrier kernel,according to one embodiment;

FIG. 41 is a flowchart showing the steps in the determination of thenumber j of the frequency components of a Zyoton and a carrier kernel,according to one embodiment;

FIG. 42 displays the absorbance spectrum of the single feature shown inFIG. 32, interpolated to 2,048 points;

FIG. 43 provides an example of the first 10 frequency componentsassociated with the interpolated feature shown in FIG. 42;

FIGS. 44A and 44B respectively show the distribution and detailedprofile of frequency components used in the construction of a carrierkernel;

FIGS. 45A-45D illustrate the distribution of carrier kernel frequenciesand their frequency components in the time and frequency domains;

FIG. 46A shows a feature; FIG. 46B shows frequency components of thefeature; and FIG. 46C shows the first ten frequency components of thefeature;

FIG. 47A-47D illustrate the distribution of frequency components of aconditioned feature after applying carrier modulation;

FIGS. 48A and 48B provide an example of a conditioned feature waveformin the time domain after modulation with a carrier kernel, and a zoom-into the first portion of the waveform;

FIG. 49 shows an example of a mapping between glucose features,non-glucose features, and Zyotons with which these features are collidedafter conditioning thereof, according to one embodiment;

FIGS. 50A-50C provide examples of different Zyoton waveforms used incollision computing, the Zyotons in the figures correspond to theZyotons referred to in FIG. 49;

FIGS. 51A-51D show the frequency domain representation of differentZyoton waveforms (corresponding to the specific Zyotons shown in FIGS.50A-50C);

FIGS. 52A-52C show the amplitude profile of sorted frequency componentsfor the Zyoton waveforms shown in FIGS. 50A-50C;

FIGS. 53A and 53B shows the power spectral density profile of anunscaled Zyoton; FIG. 53C shows an amplitude-sorted frequency componentprofile of a conditioned feature to be collided with a Zyoton;

FIGS. 54A-54C respectively show the amplitude, frequency distributionand power spectral density profile of a scaled Zyoton waveform prior toa collision; with FIG. 54C showing the power spectral density on adecibel scale;

FIGS. 55A and 55B show the full and zoom-in views of the frequencyprofile of a modified Zyoton waveform obtaining by colliding a scaledZyoton with a conditioned feature;

FIG. 56 depicts an exemplary process for determining one or moreoperating parameters of a collision computer and for generating theinputs thereof, according to one embodiment;

FIG. 57 depicts the symbolic interaction of components of a Zyoton and aconditioned feature on a synthetic collision grid;

FIGS. 58A-58D are successive pages illustrating the generation ofmodified frequency components from the collision interactions ofcomponents of an original Zyoton and a conditioned feature;

FIGS. 59A-59B are successive pages illustrating the generation ofmodified frequency components from the collision interactions ofcomponents of a different original Zyoton and a conditioned feature;

FIG. 60A is a flowchart illustrating a collision between an originalZyoton and a conditioned feature, to form a renormalized Zyoton,according to one embodiment;

FIG. 60B is a flowchart illustrating iterative collisions between arenormalized Zyoton and an original Zyoton, according to one embodiment;

FIG. 61 schematically shows an overall non-invasive measurement systemusing collision computing, according to one embodiment;

FIGS. 62 and 63 schematically show distributed non-invasive measurementsystems using collision computing, according to different embodiments;

FIG. 64 schematically shows a processing system for performing collisioncomputing and/or for providing software for collision computing,according to various embodiments;

FIG. 65 schematically shows a system for Zyoton and/or carrier kernelsynthesis, according to one embodiment;

FIG. 66 schematically shows a system for generating a projector curveset that can be used for projection of collision-computing results,according to one embodiment;

FIG. 67 illustrates other data forms that can be analyzed by collisioncomputing, according to various embodiments;

FIG. 68 schematically depicts an illumination/detection system fornon-invasive glucose measurement, according to one embodiment;

FIG. 69 schematically depicts an exemplary illumination/detection probethat can be used in the system shown in FIG. 68;

FIG. 70 schematically depicts an illumination/detection system fornon-invasive glucose measurement, according to another embodiment;

FIG. 71 shows the steps by which experimental datasets are acquiredusing a set of prepared tissue phantoms with known glucoseconcentrations and a paired set of noninvasively acquired human tissuespectra;

FIG. 72 shows how the NAG values for feature pairs are used to computethe regression slope used as a Projector Curve sub-interval;

FIG. 73 shows the steps in the generation and parameterization ofprojector curves;

FIG. 74 schematically depicts the synthesis of a projector curve setaccording to one embodiment;

FIG. 75 shows the relationship between the net, renormalized spectralenergy gains (NRSEGs) and glucose concentration in a set of tissuephantoms:

FIG. 76 shows discontinuities in the curve of the NRSEGs as a functionof glucose concentration;

FIG. 77 shows the flipped, concatenated projector curve;

FIG. 78 shows the flow for the generalized projection processimplemented to transform spectral energy changes generated in thecollision computing process into analyte concentrations;

FIG. 79 shows examples of acceptable and not-acceptable feature pairs onthe basis of their absorption gradient;

FIG. 80A shows a Projection Curve Set for an example embodiment fornon-invasively measuring glucose in human skin tissues;

FIG. 80B shows a linearized representation of a Projector Curve Set foran example embodiment for non-invasively measuring glucose;

FIG. 81 shows a composite Projection Curve for noninvasively measuringglucose in human tissue using the normalized net analyte signal obtainedusing collision computing;

FIG. 82 shows the steps in creating a Normalized Absorption Gradient(NAG) using the net, renormalized spectral energy gains (NRSEGs) fromfeature-pair data derived from human tissue spectra as inputs;

FIG. 83 shows glucose and non-glucose features in a tabular format;

FIG. 84A schematically depicts a mapping between two individualprojector curves and two projection sets, according to one embodiment;

FIG. 84B illustrates projection and measurement of an analyteconcentration using the mapping depicted in FIG. 84A;

FIG. 85 shows steps in the tissue phantom calibration curve set design;

FIG. 86 shows the steps in the use of a human calibration dataset tocomplete the projector curve set design;

FIG. 87A shows the arrangement of the layers in human skin;

FIG. 87B shows the interrogation of different layers of skin withdifferent source-detector distances;

FIG. 88 shows the distribution of photons in tissue for varyingsource-detector distances;

FIG. 89 shows the mean photon path for varying source-detectordistances;

FIG. 90 shows the difference in average depth of penetration of photonsfor skin of different thicknesses;

FIG. 91 shows a diagram of a probe with six illumination rings;

FIG. 92 shows an enlarged version of the probe from FIG. 91;

FIG. 93 shows spectra obtained for various rings of the probe in FIGS.91-92;

FIG. 94 is a detailed zoom-in into sublayers of the epidermis;

FIG. 95 shows a concentric ring based tomographic detector for sub-skintargeting;

FIG. 96 illustrates targeting a 20μ thickness section sublayer between35μ and 55μ depths;

FIG. 97 illustrates targeting a 10μ thickness section sublayer between20μ and 30μ depths;

FIG. 98 illustrates targeting a 25μ thickness sublayer section between45μ and 70μ depths;

FIGS. 99A and 99B show two portions of the patient interface to ameasurement probe;

FIG. 100 shows a Clarke Error Grid plot of comparison of a glucoseresults obtained from the arm with glucose results obtained from thefingertip;

FIG. 101 shows a Clarke Error Grid plot of comparison of a glucosemonitoring system utilizing collision computing and a reference systemused to measure blood glucose from an alternate site;

FIG. 102 shows a Clarke Error Grid plot of comparison of a glucosemonitoring system utilizing collision computing and a reference systemused to measure blood glucose from the fingertip;

FIG. 103 shows the same results as FIG. 101, using a Consensus ErrorGrid;

FIG. 104A schematically depicts an illumination/detection system fordirecting radiation to a medium and receiving radiation reflectedtherefrom, for analyte detection/quantification, according to oneembodiment;

FIG. 104B schematically depicts an illumination/detection system fordirecting radiation to a medium and receiving radiation transmittedtherethrough, for analyte detection/quantification, according to oneembodiment;

FIGS. 105A and 105B depict Michelson-type interferometers used,respectively, for transmission and reflectance measurements;

FIG. 106 depicts an example of an interferogram obtained from oneembodiment of an illumination/detection system, a correspondingintensity spectrum, and a corresponding absorbance spectrum, for use inanalyte detection/quantification;

FIG. 107 depicts features of an example absorbance spectrum of glucoseand several confounders, according to one embodiment;

FIGS. 108A and 108B show the depth of penetration of photons undervarying conditions;

FIG. 109 shows the mean photon path for skin with a thin dermis and aglucose level of 80 mg/dl;

FIG. 110 shows the mean photon path for skin with a thin dermis and aglucose level of 300 mg/dl;

FIG. 111 shows the mean photon path for skin with a thick dermis and aglucose level of 80 mg/dl;

FIG. 112 shows the mean photon path for skin with a thick dermis and aglucose level of 300 mg/dl;

FIG. 113 shows a photograph of the probe from FIGS. 91 and 92;

FIG. 114 is a photograph of a fabricated mask wheel which contains anoptical mask that selectively passes light to individual illuminationrings;

FIG. 115A shows the spectrum obtained for tissue;

FIG. 115B shows the second derivative of the spectrum in FIG. 12A;

FIG. 115C shows the second derivative spectra of protein and fat;

FIG. 116 is a schematic diagram of a dynamically-controlledillumination/detection optical system;

FIG. 117 is an illustration of an illumination/detection optical systemwith angular control;

FIG. 118A is an illustration of varying tissue illumination anddetection areas;

FIG. 118B is an illustration of varying tissue scanned volumes;

FIG. 119A is a diagram of an adjustable illumination system;

FIG. 119B is a diagram of an adjustable illumination system;

FIG. 120 is a schematic diagram illustrating how the numerical apertureof a collection fiber limits the detected photons to a cone-shapedvolume;

FIG. 121 is an example optical interface lay-out for launching lightinto the skin at an angle that varies with the illumination to detectionseparation;

FIG. 122 is an example optical interface lay-out for preferentiallydetecting light at an acceptance angle that depends on the illuminationto detection separation;

FIG. 123 is an example optical interface lay-out for both launchinglight and detecting light at various angles;

FIG. 124A depicts a plot of the distribution of detected photons from aperpendicular launch angle;

FIG. 124B depicts a plot of the distribution of detected photons from a45-degree launch angle;

FIG. 125 depicts optimization results showing the median illuminationlaunch angle versus illumination to detection separation for threedifferent skin types;

FIGS. 126A-126C illustrate the simulated distribution of lightabsorbance by layer for three different detection angles given a fixednominal 1 mm illumination to detection distance;

FIGS. 127A-127C illustrate the percent increase in reflectance vs.wavelength for detection angles ranging between 10 and 40 degrees fromvertical;

FIGS. 128A-128B depict examples of acquired spectra for glucosemeasurement in high and low noise environments;

FIGS. 129A-129F show examples of interferograms, corresponding intensityspectra, and corresponding absorbance spectra, generated in response torespective illuminations from an illumination sequence that are directedto the skin using the system shown in FIG. 68;

FIG. 130 shows the wavelengths of a selected region of features;

FIGS. 131A and 131B show the tracking between collision-computing andreference glucose results for a single patient on two visits;

FIGS. 132A and 132B show the tracking between collision-computing andreference glucose results for a second patient on two visits;

FIG. 133 shows waveforms associated with pulse plethysmography (“PPG”)measurements;

FIG. 134 shows the fundamental PPG waveform from a finger sensor;

FIGS. 135A and 135B illustrate the primary differences betweenreflective and transmissive PPG measurements;

FIG. 136A shows the LED sources and photodiodes of a PPG monitor;

FIG. 136B shows one embodiment of a PPG monitor;

FIG. 137 is a prior-art algorithm to determine heart rate based on PPGsignals;

FIGS. 138A and 138B illustrate the differences in waveform and frequencyof heart rate during stand-still and running PPG measurements;

FIGS. 139A and 139B illustrates a PPG waveform and the PPG figurecomponents as determined using a Fourier transform;

FIG. 140 illustrates the general appearance of a PPG waveform;

FIG. 141 is a flowchart of steps in an algorithm to determine heart rateusing collision computing;

FIG. 142 illustrates the window length of features used to determineheart rate using collision computing;

FIG. 143A illustrates the PPG waveform for a normal heart rate of 60beats per minute, showing the windows used to extract features forcollision-computing determination of heart rate;

FIG. 143B illustrates the PPG waveform for a slow heart rate of 30 beatsper minute, showing the windows used to extract features forcollision-computing determination of heart rate;

FIG. 143C illustrates the PPG waveform for a rapid heart rate of 120beats per minute, showing the windows used to extract features forcollision-computing determination of heart rate;

FIG. 144 shows the initial steps used to determine heart rate usingcollision computing; and

FIG. 145 shows the interaction of waveforms and renormalization of aZyoton and a conditioned feature used to determine heart rate usingcollision computing.

DETAILED DESCRIPTION Introduction

A collision computer and a collision computing process according tovarious embodiments of the invention can detect and/or quantitate ananalyte of interest within a medium, a property of a material, changesin the amount of the analyte and/or properties of the material, and/oran event or anomaly of interest. To this end, some embodiments of acollision computer receive intensity spectra representing the analyte,material, event, and/or anomaly and also the environment thereof, e.g.,a medium in which the analyte may be present. In some embodiments,radiation (e.g., near-infra red (NIR) radiation) is directed to theenvironment/medium, and the radiation reflected from or passing throughthe environment/medium is detected by a detector, and is provided as oneor more intensity spectra. In other instances, a stimulus (e.g., anelectromagnetic signal, an acoustic signal, etc.) is directed to anenvironment and one or more signals generated in response to thestimulus are obtained from one or more detectors. The frequency of theelectromagnetic signal may range from 300 EHz (where 1 exahertz orEHz=10¹⁸ Hz) down to 0.03 Hz or alternatively, with a wavelength rangingfrom 1 pm (picometer) to 10 Gm (gigameters). The detected signals aretransformed to one or more intensity spectra and are presented tovarious embodiments of a collision computer.

An intensity spectrum presented to a collision computer represents, atleast in part, an overall change in the incident radiation/stimulus thatis caused by the medium/environment. In general, the change is caused bythree factors. The first factor is the analyte and other materials thatare present in the medium/environment, including the properties of theanalyte or other materials, changes in concentration/properties of theanalyte or other materials, an event of interest, and/or an anomaly. Thesecond factor is one or more confounders, i.e., other materials that arepresent in the medium/environment and can cause a change in the incidentradiation or stimulus in a manner similar to the manner in which theanalyte causes a change. The third factor is the absorption, dispersion,and/or scattering of the incident radiation or stimulus by themedium/environment. Typically, the intensity spectra also include asignificant noise component. The noise may be introduced by sensorerrors or variability, analog-to-digital conversion (ADC) of the sensedsignal, propagation of the radiation through the medium/environmentalong different paths, etc.

Both scattering and absorption remove energy from electromagneticradiation, including light, traversing a turbid medium. Inhomogeneitiesin a specified environment scatter radiated light, to cause diffusereflection from the medium by multiple reflections with structures in orparticles of the environment. Structures in the medium act as scatteringcenters, and the overall arrangement of their shape, size, andcomposition, as well as time-varying fluctuations, including statisticalthermal fluctuations, influence the attenuation due to scattering. Thistype of scattering, where the particles are of approximately the samesize as the wavelength of light, is known as Mie scattering. Optionally,confounder molecules may also absorb energy in the same band where theanalyte absorbs energy. In various embodiments, a difference between theenergy of the incident radiation or stimulus and the energy of theintensity spectra received by a collision computer represents theoverall change in the incident radiation or stimulus. The energy of theincident radiation (and the absorbance spectrum) can be computed as thespectral energy of the incident radiation signal (and the absorbancespectrum).

As described below with reference to FIGS. 9-11, the difference betweenthe energies of the radiation incident upon the medium to be analyzedand the radiation received therefrom corresponds to one or more of thethree factors, i.e., the energy difference may include the energyabsorbed by the analyte or other materials, the energy absorbed by oneor more confounders, and/or the energy absorbed or scattered by (alsocalled lost within) the medium/environment. The energy difference mayalso be affected by one or more sources of noise described above. Invarious embodiments, a collision computer is constructed and operated todetermine the energy difference due to only the first factor, i.e.,absorption by the analyte, distinguishing such change in energy from thenoise and from the changes in energy caused by absorption by one or moreconfounders and/or due to loss in the medium/environment. A relationshipbetween the measured energy change and concentration of the analyte,property thereof, parameters of an event or anomaly, etc., can then beused to quantitate the analyte/material, properties thereof,events/anomalies, etc.

As an example of scattering, Rayleigh scattering, defined asdominantly-elastic scattering of light or other electromagneticradiation by particles much smaller than the wavelength of theradiation, generally does not involve absorption. Rayleigh scatteringcan result from the electric polarizability of the particles and may notchange the state of material. Thus, it is considered a conservativeprocess. The scattered particles may be individual atoms or molecules,and it occurs when light travels through transparent gaseous, solid, orliquid materials.

Relationship Between Zyotons and Energy

As described below, the colliding waveforms used in various embodimentsof collision computing are spatio-temporal waveforms having a timedimension and at least one spatial dimension. A spatio-temporalrepresentation of the waveform is also called a time-domainrepresentation. These waveforms can also be represented in a frequencydomain and may have one or more frequency components. The frequenciesare spatial frequencies. Spectral energy density is one measurableobservable of the waveform at various stages ofprocessing—pre-collision, post-collision, and after the renormalizationoperation that is generally required in embodiments employing severalcollision iterations. Also, the spectral energy of waveforms can becharacterized using one of more subsets of the frequency components.

In various embodiments of collision computing, a stable waveform calleda Zyoton, which may change its shape and morphology when collided withanother waveform only within limits as specified by certain parameters,is computationally collided with another waveform, called a conditionedfeature, derived from the spectral data to be analyzed. The termspectral data generally refers to any data acquired from a spectroscopicmeasurement or a spectral sensor. A spectral signal can be directlyobtained from a spectral sensor, or time-varying data can be transformedinto a spectral signal by applying a Fourier transform or othermathematical transform to the data collected over some time window. Sucha spectral signal may be referred to as a transformed signal. Aconditioned feature is obtained by modulating a pre-selected, carrierwaveform referred to as a “carrier kernel” with data (e.g., a feature).

A carrier kernel generally includes one or more (e.g., 2, 4, 6, 10, 15,1000 or more) fundamental frequencies and/or their respective harmonics,i.e., integer multiples of the fundamental frequencies. The number ofharmonics can range from 1 up to 4, 6, 10, 20, 32, 50, or more, and thenumber of included harmonics of different fundamental frequencies can bedifferent. To illustrate, an exemplary carrier kernel includes threefundamental frequencies f₀, f₁, f₂. Ten harmonics of f₀, denoted h_(0,j)for j=0 . . . 9; four harmonics of f₁, denoted h_(1,j) for j=0 . . . 3;and 15 harmonics of f₂, denoted h_(2,j) for j=0 . . . 14, are alsoincluded in this exemplary carrier kernel. Moreover, the harmonics thatare included need not start with the first harmonic, i.e., two times thefrequency of the corresponding fundamental frequency, or the firstovertone, and/or need not be consecutive. For example, only the oddharmonics of one fundamental frequency and only the even harmonics ofanother fundamental frequency may be included. In general, the harmonicscan be selected according to any specified sequence of harmonic indices,such as a geometric sequence, Fibonacci sequence, etc. The one or morefundamental frequencies and their respective harmonics that are includedin a carrier kernel are called frequency components of the carrierkernel.

The waveform resulting from the collision, called a modified Zyoton,represents, substantially, the energy loss in the radiation energyincident upon the medium due to the absorption of such energy by thepresence of the analyte of interest in the medium, or the presence ofone or more confounders in the medium, or both, specifically in thespectral region chosen for the feature. In part due to the shape andmorphology preservation properties of the Zyoton, the collision producesa modified Zyoton that can represent a change in energy substantiallyrelated only to the absorption energy loss represented by the featureused in the collision, as extracted by the collision operation.Moreover, the collision operator and one or more parameters thereof areselected such that the energy change represented by the feature isamplified when that change is represented in resulting waveformsgenerated by several iterations of the collision. Therefore, themodified Zyoton can be collided iteratively, following renormalization,with the same or different Zyotons, in order to amplify the energy lossrepresented by the feature without substantially introducing any noiseor distortion.

A modulated carrier kernel, i.e., a conditioned feature, and an originalZyoton are both traveling waveforms that can be represented in thecomputer memory. The propagation of these waveforms in space and time,and their collisions, are simulated by a programmed processor and/or byone or more hardware modules such as an application specific integratedcircuit (ASIC), a field programmable gate array (FPGA), a systolicarray, digital signal processor (DSP), etc. The result of the collision,i.e., a modified Zyoton, and the renormalized modified Zyoton derivedfrom the modified Zyoton are also traveling waveforms, each of which canbe represented in the computer memory. In various embodiments, thepropagation of the renormalized modified Zyoton in space and collisionthereof with the original Zyoton or another Zyoton are also simulatedusing a programmed processor and/or one or more hardware modules.

Typically, the medium being observed contains one or more analytes ofinterest that need to be characterized qualitatively or quantitatively.It may also have other substances present that are not of interest butspectroscopically absorb, emit, fluoresce, or otherwise interfere withthe analyte signal in the data region chosen, in the same bands as theanalyte, and may thereby act as confounders to the measurement ofanalytes of interest. The collision computing paradigm described herecan be applied for detecting and characterizing analytes inconcentrations from as high as moles/l or higher to concentrations aslow as picomoles/l or even lower. Individually or collectively,confounders may be present with many orders of magnitude greaterconcentration compared to analytes of interest. For example, theconcentration of glucose, a biochemical blood analyte of interest, canbe overshadowed by the concentrations of many other substances presentin blood or interstitial fluid.

Zyotons are conditioned feature-complement collision waveforms that areconstructed to function as energy amplification mechanisms. Zyotons maybe constructed using a variety of waveform families and generatorfunction families suitable for detecting an analyte or compound ofinterest. Useful waveform families include, but are not limited to:solitons; autosolitons; similaritons; custom solitons generated using asine-Gordon-based equation; self-compressing similaritons;vortex-solitons; multi-color solitons; parabolic-similaritons; Riccisolitons; wavelets; curvelets; ridgelets; bions; elliptic wavesincluding either or both of Jacobi elliptic functions and Weierstrasselliptic functions; and nonautonomous similinear wave equations.

Useful Zyoton generator function families include, but are not limitedto: meromorphic functions; Gamma functions; Riemann Zeta functions;regular instantons; Frobenius manifolds; harmonic oscillators; Hermitepolynomials; polynomial sequences; asymptotic Hankel functions; Besselfunctions; fractals; Neumann functions (spherical); poweroid coupledwith sinusoidal functions; spatial random fields; cyclostationaryseries; random number generators; spherical harmonics; chaoticattractors; exponential attractors; multipoint Krylov-subspaceprojectors; Lyapunov functions; inertial manifolds of Navier-Stokesequation; evolution equation for polynomial nonlinear reaction-diffusionequation; evolution equation for Kuramoto-Savashinsky equation;evolution equation of exponential attractors; Fourier series; andRamanuj an theta functions.

Random number generators (RNG) are also useful as generator functions toproduce numerical sequences used to synthesize Zyotons. Desirablegeneral properties of RNG used to develop Zyotons include replicability(i.e., generated number sequences would be replicable if the seeds usedto generate the random numbers were known and fixed), and the longestpractical cycle length or periodicity (i.e., the longest possible timebefore numbers in the generated sequence start to repeat). Otherattributes such as independence (i.e., correlation between numbersgenerated by the RNG), uniformity, and computational speed are optionalfor the purpose of developing Zyotons. Classes of RNG that are used todevelop Zyotons, in which r_(n) is the random number generated, includelinear congruential generators, (where r_(n)=(ar_(n−1)+c) mod m, n=1, 2,. . . ; where m>0 is an integer coefficient used in the modulusoperation, and a period up to 2³¹), multiplicative congruentialgenerators (where r_(n)=(ar_(n−1)) mod m, m>0, n=1, 2, . . . and aperiod up to 2³¹−2), and additive congruential generators or FibonacciRNG generators (where r_(n)=(r_(n−1)+r_(n−k)) mod m, n=1, 2, . . . ;m>0; k≧2 and with a period up to m^(k)).

RNG based on linear, multiplicative, or additive congruential generatorsmay be used as Zyoton generator functions even though they can producenumbers that are not random (also known as pseudorandom), and can berelatively more easily controlled (compared to other methods) to exhibitdesired spectral properties in the frequency domain, and thus can beused as a first step to generate numerical sequences used for thesynthesis of one or more Zyotons.

Regardless of the generator function used, the generated numbers arecollected, fixed (or “frozen”), and then Fourier transformed tofrequency distributions with desired properties and amplitude profilesthat are useful as Zyotons. RNG are particularly useful for developingcollections of related Zyotons (with some common underlying propertiesin the frequency domain) but where each subsequent collision uses adifferent Zyoton from such a collection of Zyotons in multiple-iterationcollision sequences.

The polynomial sequences described above typically are a sequence ofpolynomials indexed by the nonnegative integers 0, 1, 2, 3, . . . , inwhich each index is equal to the degree of the corresponding polynomial.Finite and infinite length numerical sequences can be encoded aspolynomial sequences and can be Fourier transformed, and aredifferentiable and integrable and can be represented as continuousgeometrical curves and manifolds. Zyotons generated using polynomialsequences can encode arbitrary numerical sequences of interest.Specifically, arbitrarily desired frequency component patterns can beencoded using polynomial sequences. Specific examples of polynomialsequences that can be used as Zyoton generators include Abel polynomials(where n-th term of the polynomial is of the formp_(n)(x)=x(x−an)^(n−1)), and Bell polynomials given by:

$\begin{matrix}{{{B_{n,k}\left( {x_{1},x_{2},\ldots\mspace{14mu},x_{n - k + 1}} \right)} = {\sum\;{\frac{n!}{{j_{1}!}{j_{2}!}\mspace{14mu}\cdots\mspace{14mu}{j_{n - k + 1}!}}\left( \frac{x_{1}}{1!} \right)^{j\; 1}\left( \frac{x_{2}}{2!} \right)^{j\; 2}{\cdots\left( \frac{x_{n - k + 1}}{\left( {n - k + 1} \right)!} \right)}^{j_{n - k + 1}}}}},} & (1)\end{matrix}$where the sum is taken over all sequences j₁, j₂, j₃, . . . , j_(n−k+1)of non-negative integers such that:j ₁ +j ₂ + . . . +j _(n−k+1) =k and j ₁+2j ₂+3j ₃+ . . . +(n−k+1)j_(n−k+1) =n.  (2)As an example, Abel and Bell polynomials can be used to encodecombinatorial sets of frequencies (such as the k, m, and j frequencycomponent groups referred to below), and then Fourier transformed toderive Zyoton waveforms which can be used in collisions.

Zyotons can also be created by combining other individual Zyotons, e.g.,by multiplying, adding, or phase-shifting (also called subtracting), twoor more individual Zyotons. Generation of new Zyotons by dividing orsubtracting one Zyoton waveform from another Zyoton waveform can beachieved by using multiplication or addition operation respectively.Zyotons so combined to form a new Zyoton can be from the same ordifferent families of Zyotons. In addition, various waveform functionsand numerical sequences generated by a sequence generator can betransformed or reduced to any of the functions listed above. Such otherwaveforms and/or numerical sequences, which can be transformed orreduced into a waveform family/numerical sequence that is suitable forZyoton synthesis, may be used to synthesize a Zyoton to be used in thecollision process.

Although waveforms derived from all the above families can propagate ina constant medium without substantial change to their morphology,Zyotons derived from the families of optical solitons, autosolitons,similaritons, custom solitons, self-compressing similaritons,vortex-solitons, multi-color solitons, parabolic-similaritons and Riccisolitons generally retain their morphology and exhibit post-collisionpropagation properties substantially similar to their pre-collisionpropagation properties.

The above-described pattern-forming systems may be used as generatorfunctions to derive a Zyoton waveform based on three factors: (i) theirtendency to produce spatially confined states on the same time-domainspatial (i.e., morphological) and spectral scale as the entire set ofanticipated feature waveforms from a spectroscopic sensor, ascharacterized by the spectral bandwidth, spectral envelope, peak energy,and amplitude distribution; (ii) non-stationarity of confounders, i.e.,are they constant or time-varying in concentration during themeasurement process resulting in changes in the signal-to-clutterincrease required for an accurate measurement; and (iii)cyclostationarity of feature data itself, i.e., degree to which thestatistical properties of the feature change over time, as describedbelow, including the morphology of the amplitudes of the feature in thetime domain, distribution of spatial frequencies of the feature anddistribution of relative amplitudes of frequencies in the frequencydomain, and any phase rotation of the waveform in the frequency domain.

A purpose of modulation of a carrier kernel by a feature, which may bepreceded by an optional precursor frequency modulation, is to achieve adesired level of cyclostationarity or poly-cyclostationarity in theconditioned feature waveform, and to force the conditioned featurewaveform to be represented using a combination of one or more periodic(e.g., sigmoidal) functions. Poly-cyclostationarity can increase theprobability of inducing and detecting morphological changespost-collision in specific frequency components. Carrier kernelwaveforms with higher frequencies than those of the feature (or theoptionally modulated feature) are generally used in the featuremodulation step, to condition features by inducing poly-cyclostationaryproperties.

In summary, Zyotons can be represented as localized traveling-wavepackets, which exist as propagating entities through space and/or time.In general, the space and/or time propagation of Zyoton waveforms isscale and shift invariant. As such, transformations may be used to varyspace and/or time scales to match the precision and accuracy desired inthe data-collection domain, and/or the spectral resolution of sensorsproducing the feature data. For features with low cyclo-stationarity,complex or more nuanced generator functions may be required, such asLyapunov functions or meromorphic functions.

In one exemplary embodiment that can be used for non-invasive glucoseanalyte detection and measurement, Zyotons are derived using a basefamily of mathematical functions denoted as solitons. This choice ofsolitons as source family generator for Zyoton derivation, in general,is based on the above three properties for selection of waveforms, butis strongly influenced by the stationary nature of confounders in thedata during the course of measurement (generally over a time period of afew milliseconds to a few seconds). Solitons are defined and representedas a permanent localized disturbance in a linear or non-linear wave. Inphysical systems, such as propagation of light waves in an opticalfiber, solitons can result from the offsetting of nonlinear anddispersive effects in the propagation medium. Mathematically, solitonsare a solution to weakly nonlinear dispersive partial differentialequations describing physical systems, such as optical energypropagation in a telecommunication fiber cable. A detailed treatment andbackground to soliton dynamics is provided in Ablowitz, Mark J.,Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons (CambridgeTexts in Applied Mathematics) (2011), and in Dauxois, T. and Peyrard,M., Physics of Solitons, ISBN-13: 978-0521854214.

Properties that make solitons attractive as a base family for designingcollision waveforms or Zyotons include first, localization of the centerof mass or confinement of peak energy to a region and resistance to weakexternal perturbations. Since collision computing involves deconstructeddata or spectral features (i.e., fragments of spectra), local energyabsorption or losses, and locality and stability of the soliton waveformare generally important. Second, permanency or morphological stabilityis important—solitons retain their shape. The accurate determination ofspectral energy changes in the post-collision waveform, due to energytransfer from the colliding waveforms to the post-collision collidedentity (i.e., the modified Zyoton), is important to analyteconcentration estimation.

Power spectral density (PSD) of a signal waveform can be defined as thepower contributed to the wave by a frequency, per unit frequency inwatts/hertz (W/Hz). The PSD is the normalized limit of the energyspectral density (ESD) for a windowed signal x_(N)(t) and a measure ofdistribution of signal power. Thus, spectral energy corresponds to thetotal power within a frequency or wavelength interval. Alternately,spectral energy can also be computed for a set of discrete frequencycomponents by using the power spectral density of the selected frequencycomponents. This definition of power spectral density generalizes theestimation of total spectral energy S_(xx)(ω) for a discretized anddigitized signal waveform (e.g., feature data), represented as a finitetime-series x_(n) with 1≦n≦N, such as a signal sampled at discrete timesx_(n)=x(nΔt) for a total measurement period T=NΔt. The spectral energyis given by:

$\begin{matrix}{{S_{xx}(\omega)} = {\frac{\left( {\Delta\; t} \right)^{2}}{T}{{\sum\limits_{n = 1}^{N}\;{x_{n}{\mathbb{e}}^{{- i}\;\omega\; n}}}}^{2}}} & (3)\end{matrix}$where ω=2πf, and f denotes the frequency of the signal.

Given that mathematically one can compute the spectral energy densityand the spectral energy for a signal waveform, waveform propagation andwaveform collisions can be represented as energy entities and energytransfer operations, respectively. As Zyoton collisions are inherentlynon-linear events, energy representation provides a mathematicalframework (or an “energy algebra”) for describing and inducing complexbehaviors. Collision computing as described herein facilitates detectionand/or quantitation of analytes and events using energy algebra.Morphological stability and properties of entire Zyotons, or selectedfrequency components with high retained fidelity, allows comparison andcharacterization both before and after collisions for large numbers offeatures extracted from large numbers of samples, collected undersimilar conditions, using the same or similar hardware platform andsensors.

Solitons are described in the art as “waves that act like particles.” Anindividual soliton can travel through a propagation medium over acertain distance without distortion of the soliton's morphology andwithout dissipation of the soliton's energy. If one soliton collideswith another, typically the morphology of both solitons is preservedafter the collision, and only a phase shift occurs in the respectivepropagation of one or both solitons as they continue to propagatethrough the propagation medium. Phase shift in this context generallymeans that there is an offset in arrival time and phase for either oneor both of the colliding solitons relative to the case when no collisionoccurs, and a phase shift does not introduce any new waveform frequencycomponents that would alter energies of the two solitons. As such, nosignificant (e.g., more than 0.01%) change generally occurs in therespective energies of the two solitons after a collision between them.In contrast, the morphological envelope of a soliton generally changesduring collision with a non-soliton travelling wave. Typically, if asoliton collides with a non-soliton waveform of similar energy, thesoliton is destroyed. Thus, in the first interaction (i.e., between twosolitons), no measurable energy transfer occurs between the two solitonsand, in the second interaction (i.e., between a soliton and anon-soliton waveform), although energy transfer occurs, it cannot bemeasured because the soliton is destroyed during the collision.

The selection of a soliton family to construct a Zyoton, and itstime-domain and frequency-domain parameterization, is based on theconsideration of at least one of several specific attributes, whichinclude: the signal-to-noise ratio (SNR) of the measurement system, theanticipated signal-to-clutter ratio (SCR) or signal-to-clutter noiseratio (SCNR), the degree of desired SCR increase, the desired analytequantitation accuracy and precision, resolution, specificity, dynamicrange, sensitivity, and concentration range over which linearity isdesired. The SCNR (signal to clutter noise power ratio or signal tocoherent noise power ratio) is generally defined as the ratio of signalpower to the power of the sum of clutter plus background non-coherentnoise power. Clutter can be due to signal from confounders or fromcoherent noise. Coherent noise is a type of smooth pseudorandom noisewhich has been usually defined in the art as having three properties:(i) passing in the same input value will always return the same outputvalue; (ii) a small change in the input value will produce a smallchange in the output value; and (iii) a large change in the input valuewill produce a random change in the output value. The sources of suchcoherent noise include: variability due to free space optics (i.e.,variability in the radiated and/or collected light traveling through airas it is subjected to variable amounts of water vapor), detectorelectronic noise, light drift and variability, variable absorptionthrough a fiber optic probe, etc.

As described above, a conditioned feature is particularly constructed torepresent the energy absorbed by an analyte or by one or moreconfounders, and accurate estimation of the absorbed energies can leadto an accurate estimation of the analyte concentration. To facilitateaccurate estimation of the absorbed energy represented in a conditionedfeature in various embodiments, particularly designed Zyotons areemployed. Specifically, a Zyoton is modified after a collision with aconditioned feature but the modification is particularly controlled suchthat the original Zyoton is transformed into a modified Zyoton thatcontinues to propagate thorough the propagation medium and is notdestroyed at least over a certain propagation distance. Therefore, theenergy transferred to the original Zyoton during the collision can bemeasured from the modified Zyoton. As described below, the Zyoton andthe conditioned feature are synthesized in a co-dependent manner, suchthat the energy transferred to the Zyoton over one or more collisioniterations is proportional to the energy absorbed by an analyte and/orone or more confounders, as represented by the conditioned feature. Thepermanency or morphological stability of a Zyoton is important, ingeneral, to properly estimate spectral energy changes therein, which arerelated to the analyte presence or concentration at the feature level.As described below, the energy changes at the feature level may beaggregated to estimate the net energy change due to the presence andquantity of an analyte.

Collisions between conditioned features and Zyotons lead to minorwaveform distortions of the Zyoton that can be used to performpost-collision energy computations, because energy transfer is possiblebetween a conditioned feature and a Zyoton. Therefore, the feature,derived from incoming or acquired data, generally acts as an energymodulator to the Zyoton. Propagation over grids with a sufficient numberof points and over sufficient travel distances can filter outpost-collision transients and dispersion in high frequency,lower-amplitude peaks. Typically, multiple collision iterations betweena conditioned feature and a Zyoton or between a modified Zyoton and aZyoton are involved in collision-based energy absorption estimation. Soeach post-collision result is a modified or energy-amplified Zyoton.Specifically, as described above, as a result of a collision between anoriginal Zyoton and a conditioned feature, a modified Zyoton withincreased energy is obtained. The amount of energy amplification duringa collision is related to the properties of the conditioned feature,e.g., energy absorption at NIR wavelengths due to analyte concentrationin the medium irradiated with NIR. The increase in energy is generallyrelated to the energy absorbed by an analyte and/or one or moreconfounders, as represented by the conditioned feature. The absorbedenergy can also be referred to as energy loss or energy lost as a resultof the presence of the analyte and/or one or more confounders. As usedherein, the absorbed energy or energy loss, however, relates only toanalytes and/or confounder(s) and not to energy otherwise dispersed orlost in the environment or medium. It should be understood that a mediumto be analyzed in which an analyte and one or more confounders may bepresent may be different than a propagation medium in which Zyoton(s)and conditioned feature(s) propagate.

In some embodiments, the modified Zyoton is renormalized as describedbelow, and the renormalized Zyoton is collided with the original Zyoton.The result of this subsequent collision is another modified Zyoton,typically with more energy than the original Zyoton and the previouslygenerated modified Zyoton and, again, the increase in the energy isrelated to the energy absorbed by an analyte and/or one or moreconfounders. In general, successive collisions between the originalZyoton and the modified, renormalized Zyotons can result in recurringenergy increases in the modified Zyotons that relate to the energyabsorbed by an analyte and/or one or more confounders, with increasingaccuracy and observability. Thus, after a specified number of collisioniterations, the energy gain in a modified Zyoton relative to theoriginal Zyoton can be equivalent to or a multiple of the energy loss orthe absorbed energy represented by a feature and/or a conditionedfeature. Through one or more (e.g., tens, hundreds, thousands, tens ofthousands, or more) collision iterations, it is important thatunderlying properties of the original and successively modified Zyotonsare maintained, i.e., the morphological characteristics thereof changein a controlled manner, to enable accurate post-collision energycomputations. Normal, non-solition waves generally flatten out, leadingto loss of or change in character of dominant frequency components,thereby rendering post-collision energy computations ineffectual.

Assume that the total energy of the original Zyoton is E and that theenergy of a conditioned feature is e. Further, assume that e includesthe energy Δe, where Δe actually represents a cumulative loss of energydue to absorbance by an analyte and/or one or more confounders in themedium. Prior to the first collision, e is set to be around 0.001 timesE and the gain in any individual collision iteration i, denoted δe_(i),is less than 10⁻⁶ E. In the table below, δe₁ represents the gain in thepost-collision spectral energy of the modified Zyoton due to transferfrom the conditioned feature after the first collision, prior to therenormalization step. Similarly, δe_(i) represents the gain in thepost-collision spectral energy of the modified Zyoton due to transferfrom the modified Zyoton after the i^(th) collision, prior to therenormalization step. This gain, δe_(i), is related to the NIRabsorption by the analyte, within the wavelength boundary defining thefeature. As described below, the collision computing process is designedso that the estimated per collision gain of δe_(i) is proportional tothe absorption of energy by the concentration of analyte in the medium.This proportional relationship of E to δe_(i) (between a Zyoton and arenormalized Zyoton after the first collision iteration) is maintainedthroughout subsequent collisions, as shown below.

TABLE 2 Energy of Renormalized Post- Zyoton (Energy Collision Energy ofof Conditioned Energy of Iteration/ Original Feature for ModifiedCollision Zyoton Iteration 1) Zyoton Comment 1 E e E + δe₁ δe₁ > 0 2 Eδe₁ E + δe₂ δe₂ ≧ δe₁ 3 E δe₂ E + δe₃ δe₃ ≧ δe₂

E

E +  

δe_(ℕ) ≥ δe_(ℕ − 1) ≈ Δe

The number of iterations/collisions

is selected such that after

iterations/collisions, the increase in the energy of the originalZyoton, given by

is approximately equal to Δe, or is a multiple thereof, i.e., the netloss of energy due to absorbance by an analyte and/or one or moreconfounders. Also, to preserve the propagation integrity of the Zyoton,the frequency components of the carrier kernel are scaled and selectedto establish the spectral energy of the conditioned feature waveform tobe around 1/100^(th), 1/1,000^(th), or 1/100,000^(th) of that of theZyoton for the selected wavelength interval, so the feature serves onlyas a weak perturbation to the Zyoton.

The process of conditioning data features and the generation of Zyotonsand their parameterization is driven by the overall analysisobjectives—often detection of energy absorption by the analyte—andrequires any conditioned features (in some cases just a single feature)and their Zyotons to become co-dependent. The feature conditioning andthe Zyoton selection are both dependent on the expectedsignal-to-clutter ratio (SCR) improvement required, as described above.This co-dependency is captured by the frequency bandwidth and frequencycomponents of both the carrier kernel used in feature conditioning andby the selection of Zyotons. The frequency bandwidth of the carrierkernel is generally set to be between

${\frac{1}{({SCR})^{2}}\mspace{14mu}{and}\mspace{14mu}\frac{1}{({SCR})^{3}}},$so a measurement with a SCR of 0.01 would require a carrier kernelbandwidth of 10⁴ to 10⁶ Hz. A carrier kernel bandwidth of 100 KHz can beused in the analysis of spectroscopic data for a non-invasive glucosemonitoring application, for example.

The total set of power-sorted frequency components for the Zyoton isdefined as H=k+m+j where k>0, m≧0, and j>0, and the k and j frequencycomponents do not overlap. In general, the k components are related toabsorption by the analyte and are called analyte-informationrepresenting components, the j components are generally related to theenergy lost due to scattering and are called non-analyte informationrepresenting components, and the m components serve as a transition zoneto the j components, and are called transition components. In general,non-analyte information can be noise, clutter, etc., that this itselfcan be considered to be information, e.g., about noise, clutter, etc.Therefore, analyte-information-representing generally means representinga property, such as the presence or absence of or a quantity of ananalyte and/or one or more confounders, energy absorbed by the analyteand/or one or more confounders, etc.

In various embodiments, the amplitudes of the analyte-representing kfrequency components are higher relative to the amplitudes of the m andj components and, as such, in these embodiments, the k components arealso called high-energy components. The non-analyte informationrepresenting j frequency components may have low amplitudes relative tothe amplitudes of the k and m components, and may be called low-energycomponents. The transition components, i.e., the m frequency components,may have amplitudes greater than the amplitudes of the j components butlower than the amplitudes of the k components, and may be calledmedium-energy components. In some embodiments, the Zyotons and thecorresponding carrier kernels are synthesized such that theanalyte-information representing k components of the Zyoton and theco-dependent conditioned feature(s) are low-energy components, and thenon-analyte information representing j components of the Zyoton and theco-dependent conditioned feature(s) are high-energy components.

Typically, the high-energy components of a Zyoton and the conditionedfeature(s) have spectral energy that is several orders of magnitudegreater than the spectral energy of the low-energy components, and themedium-energy components have spectral energy that is a multiple of thespectral energy of the low-energy components but that is not more thanan order of magnitude greater than the spectral energy of the low-energycomponents. In some embodiments, the frequency components of the Zyoton(and also of the conditioned feature) can have amplitudes that can berepresented by a continuum, where these are not broken up into specifiedk, m, and j subsets, each corresponding to a particular energy band.Instead, in these embodiments, certain frequency components can beselected which correspond to energy absorbed by an analyte, while otherfrequency components can be selected which correspond to absorption byconfounders or sources of random noise, such as scattering or absorptionvariations of a confounder. Those frequency components corresponding toenergy absorbed by an analyte may be amplified during the collisioncomputing process, while those corresponding to noise may not beamplified.

The choice of the number k of the frequency components used in thespectral energy computations is driven in part by the dynamic range ofspectral energy change desired across the dynamic range of concentrationof the analyte of interest, and the desired precision. Example values ofk range from 4 through 256 when a carrier kernel with a bandwidth of 100KHz is used. The value of m ranges, for example, between 0 and amultiple of k, such as (4×k). Example values used in non-invasiveglucose measurement are k=6 and m=8.

As described above, Zyotons may be selected from generator functionsand/or waveform families that can produce waveforms that retain theirproperties, e.g., solitons that are stable over the desired frequencybandwidth. As such, and as further described below, the Zyoton and theconditioned feature waveforms, collectively referred to as the collisionentities, are co-dependent. The energy scaling relationship between theZyoton and the conditioned feature imposes the co-dependency conditionbetween the two waveforms; and the scaling step as part ofrenormalization between the Zyoton and the modified Zyoton (prior to thesecond and any subsequent collisions) can re-establish the co-dependencycondition between those two. Thus, by the algebraic transitive closureproperty, the Zyoton, the conditioned feature, the modified Zyoton, andthe renormalized Zyoton are co-dependent.

As an example, one-dimensional Zyotons existing as a function of time t,Z_(N)(xt), can be constructed as:Z _(N)(xt)=2∂_(x) TrB _(x)(1+B)⁻¹  (4)

where B is an N×N matrix with elements

${B_{mn} = {\frac{1}{p_{m} + p_{n}}C_{m}C_{n}}},$

with variables C_(m), C_(n) defined as

${C_{m} = {\exp\left\{ {s_{m\;} - {\frac{1}{2\;}\ln\;{{ia}_{m}}}} \right\}}},{C_{n} = {\exp\left\{ {s_{n\;} - {\frac{1}{2\;}\ln\;{{ia}_{n}}}} \right\}}},$respectively with m, n≦N;

${s_{m} = {{p_{m}x} - {p_{m}^{3}t} + \delta_{m}}},{{ia}_{m} = {\prod\limits_{n{({\neq m})}}\;{\frac{p_{m} - p_{n}}{p_{m} + p_{n}}\frac{1}{2\; p_{m}}}}},$

-   -   and δ_(m) is a real-number constant,    -   p_(m) is a positive constant such that p₁>p₂> . . . >p_(N).

The selection of p_(m) and δ_(m) in the equations above is not based onthe bandwidth of the Zyoton waveform but, instead, is based on thedesired amplitude ratio of b sideband peaks on the left and right of theprimary amplitude peak as shown in FIGS. 12A-12C. Note that b sidebandpeaks for the Zyoton waveform are defined as the portion of Zyoton waveamplitudes that are either above or below the frequency componentcorresponding to the peak amplitude of Z_(N)(xt). In the above equationfor Z_(N)(xt), Tr is an algebraic operator that denotes the trace of ann-by-n square matrix and is defined to be the sum of the elements on themain diagonal of the matrix (the diagonal from the upper left to thelower right) of A, i.e.,

${{tr}\;(A)} = {{a_{11} + a_{22} + \cdots + a_{nn}} = {\sum\limits_{i = 1}^{n}\; a_{ii}}}$where a_(nn) denotes the entry on the n-th row and n-th column of A.This is an example of a Zyoton kernel that can be used for glucoseanalysis.

Overview of a Measurement System

With reference to FIG. 13, a typical process of detecting the presenceof an analyte in a medium and/or quantifying an amount of the analyte inthe medium includes acquiring one or more intensity spectra in step 2.Using spectra and the corresponding reference concentration data (alsocalled a reference calibration dataset) that is obtained in step 14, atleast in part, from known amounts or concentrations of analyte, thepresence of the analyte is detected and/or the quantity thereof isestimated in step 16 via a projection process that uses calibrationtables, sets, and/or curves included in the reference calibrationdataset. The presence of the analyte and/or the estimated quantitythereof is determined and reported in steps 18, 20.

The method described here utilizes one or more nonlinear, non-invertiblecomputational collisions between two entities—a feature derived andextracted from sample observations, and a purposefully constructedwaveform, where the collision yields waveforms that can be processed todetermine analyte presence and to estimate analyte concentrations in theuncharacterized samples. This method of detecting the presence andestimating concentration of analytes from sensor data is performed bytransforming the incoming sensor data to a wavefront called conditionedfeature (Ψ_(CF)) (steps 4, 8); selecting another waveform, referred toas the Zyoton (Ψ_(Z)) (step 6); colliding the conditioned feature withthe Zyoton to obtain a modified Zyoton (Ψ_(Z′)) and/or renormalizedZyoton (Ψ_(Z″)) (step 10), which may include additional collisioniterations; and assessing the properties of the spectral energydistribution of the modified and/or renormalized Zyoton (also called acoupled waveform complex) (step 12). The step 12 generally includesdetermining the total spectral energy transferred to the Zyoton from theanalyte-information representing components of the conditioned featurewaveform after the collision. The wavelengths used in the synthesis ofthe Zyoton(s), and that may be present in the co-dependent conditionedfeature and the modified and renormalized Zyoton waveforms are nottypically the wavelengths associated with the incoming sensor data.

The conditioned-feature waveforms are “domain-based”, in that they arederived from features, which have themselves been derived from signals,spectral data, or sensor data in the data-collection domain. TheZyotons, however, are “non-domain-based” or are independent of thedata-collection domain in that the waveform kernels they are synthesizedfrom may have no direct relationship to the sensor data acquired in thedata collection domain. For example, data collected can be of the formNIR radiation, heat radiation, visible light, etc., while a Zyoton canbe generated from various waveform families and/or generator functionsthat waveforms and functions unrelated to these data domains.

Zyotons represent models of physical waveforms encountered in domainsdifferent from the data-collection domain (e.g., solitons in opticalcommunication or cryptography). Non-domain generator functions may beoptionally used to construct Zyotons where the generator functions areeither closed-form analytical functions (such as Gamma functions,Riemann Zeta functions, Neumann Functions) or are represented as formalpower series (e.g., Lambert series, Dirichlet series) in oneindeterminate variable, whose coefficients encode information about asequence of numbers that is indexed by the natural numbers. Zyotons,such as those derived from spherical harmonics, can be optionallyderived from generator functions represented as formal power series inmore than one indeterminate variable, to encode information about arraysof numbers indexed by several natural numbers. While these waveformfamilies and the generator functions can be mathematical entities(generally functions and sequences), the particular frequencies of theZyotons are selected, however, according to the properties of theanalyte, the properties of one or more confounders, the properties ofthe medium/environment to be analyzed, and/or the properties of themeasurement system.

The spectral energy distribution used in the step 12 for the detectionand/or quantitation of the analyte can be described as the distributionof flux density versus frequency or spatial wavelength, or the energy asa function of the spatial wavelength. Depending on the nature of theinput data, the characteristics of the sensor used for observing theanalyte, the complexity and concentration of confounders, and theexpected concentration of the analyte, one or more computationalcollisions may be implemented by the method described herein. After eachcollision iteration, the power spectral energy distribution of thecollision-modified Zyoton (the resulting waveform: Ψ_(Z′)) is computedand compared to the power spectral density of the original Zyotonwaveform to determine that the codependency condition (described below)is still met. The waveform collisions may be implemented either in theanalog or digital computing domain, and in a time domain or in afrequency domain. Analyte presence and concentration are determinedbased on the net gain (which can also be represented as an energy lossin some computer implementations) in the spectral energy computed fromspectral energy distribution of the modified and/or renormalized Zyotonafter a selected number of collision iterations.

The computation of the spectral energy changes requires observability ofenergy states of the pre- and post-collision waveforms. As introduced inclassical control theory, in general, “observability” is a measure ofhow well internal states of a system can be inferred by knowledge of itsexternal, measurable outputs or observables. In some embodimentsdescribed herein, the frequency-domain amplitudes of the pre-collisionoriginal Zyoton and, post-collision, the frequency-domain amplitudes ofthe modified Zyoton and renormalized Zyoton waveforms are treated assystem or “collision observables.” The collision process is implementedsuch that collision observables can be computed and compared whenfeatures are extracted from different measurements of the sample withdifferent material concentrations, per the precision requirements of thesystem.

If a Zyoton does not possess the desirable properties described above,the collision observables, harvested from a single collision or fromseveral collision iterations would offer no inferential utility i.e.,the ability to determine the presence of and to estimate theconcentration of materials in unknown, uncharacterized samples. Insteadthe computed spectral energy values may appear as random artifacts ornoise given the very low signal-to-clutter ratios in the measuredsamples. The ability to observe consistent patterns in the spectralenergy gained (or lost) after each collision iteration between twocolliding waveforms is a prerequisite to concluding the integrity andconsistency of the collision process. As described below, this isachieved, in part, by maintaining co-dependency between the collidingwaveforms. The typical conditions for Zyoton synthesis (e.g., spectralenergy 10³ or 10⁴ times higher than that of the conditioned feature) mayset bounds for the changes in observed spectral energy after eachcollision.

The processing unit where the collisions are implemented is denoted asthe collision computer. Three key elements of collision computing are:(i) the collision process on data, including the design of the collisionwaveforms, the collision operator, and number of collision iterationsrequired to achieve the desired detection performance; (ii) thepreprocessing of the acquired spectroscopic data, includingdeconstruction into spectral fragments that are a subset of the spectrumand their conditioning for use in the collision process; and (iii) thepost-collision estimation of the change in spectral energy of the systemas a mechanism to estimate the total energy change due to absorption bythe analyte and its use to estimate analyte concentration.

An example of source data includes an intensity spectrum acquired bydirecting radiation to a medium and by detecting or collecting radiationreflected by the medium, or by directing radiation through a medium anddetecting the transmitted radiation. In step 4, the spectral data may benormalized to eliminate amplitude variations, and one or more features(selected wavelength ranges of a spectrum) may be extracted from theoptionally normalized spectral data. Different Zyotons may be requiredto collide with different features. The spectral energy of the Zyotonshould be matched to both the spectral energy and the amplitude of thefeature as described herein.

One or more Zyotons, with which the conditioned features arecomputationally collided to enable detection and/or measurement of theanalyte, are generated or obtained in step 6. The Zyotons are generatedaccording to one or more of the requirements for precision, accuracy,limit of detection, limit of quantization of desired analysis results,and characteristics of the spectral data acquisition system including:signal-to-noise ratio (SNR), system stability, spectral resolution,spectral bandwidth, illumination process and spatial sequence (if used),expected signal-to-clutter ratio, (SCR) due to the presence ofconfounders in the medium to be analyzed, and the requiredsignal-to-clutter increase for an accurate measurement. As Zyotons arederived from inherently stable waveforms, the chromatic dispersion ofthe Zyoton waveform, the peak power and pulse energy (defined as theproduct of the power of the waveform peak and its width or the areaunder the peak) in its first k peak-power sorted frequency components(where k is typically <6), collectively control the limit of detectionand quantitation that can be achieved in one or more collisions. Invarious embodiments, a reference to the “k frequency components”generally describes the first k peak-power-sorted frequency componentsof a waveform such as a Zyoton, a carrier kernel, and a conditionedfeature.

In step 8, the features extracted in step 4 are conditioned, so thatZyotons and the conditioned features become co-dependent. Collectively,we refer below to the constraints on co-dependency imposed by thevariables κ_(DV1), κ_(DV2), κ_(DV3), and κ^(SYN) as the “Kappa Test.”Depending on whether the testing and/or scaling is performed in the timedomain or in the frequency domain, a domain-specific value of theapplicable Kappa variable is used for various tests of co-dependency invarious embodiments.

In a waveform obtained by combining two or more sinusoids, such as inthe construction of a Zyoton, construction of conditioned feature, etc.,phase velocity is the velocity of a particular phase of the waveform andcan be expressed as a ratio of the wave's angular frequency overwavenumber,

${i.e.},\;{v_{p} = {\frac{\omega}{k}.}}$For Zyotons constructed using soliton waveforms, the dispersion velocityis same as their phase velocity. In contrast, group velocity is thephase velocity of an envelope representing the combination of the two ormore sinusoids, and can be expressed as

$v_{g} = {\frac{\mathbb{d}\omega}{\mathbb{d}k}.}$The dispersion velocities of a Zyoton and a conditioned feature aregenerally proportional to the time domain amplitudes of the sidebandpeaks thereof.

Assume that during the collision process, a conditioned feature waveformCF_(i), corresponding to a feature F_(i), is propagating with dispersionvelocity ω₁, and a Zyoton Z_(i) is propagating with dispersion velocityω₂. Further assume that the collision of the two waveforms produced amodified Zyoton Z_(i)′, propagating with dispersion velocity ω₃. Thedifference between the pre- and post-collision dispersion velocities ofthe Zyotons, i.e., the magnitude of (ω₂−ω₃) should be less than a presetKappa parameter κ_(DV3), if the conditioned feature waveform CF_(i) andthe original Zyoton Z_(i) are co-dependent. If a Kappa test is performedin the time domain, the velocity can be obtained as either the L1 normor the L2 norm of the time-domain amplitudes of a selected number ofsideband peaks of the two Zyoton waveforms Z_(i) and Z′_(i).

Optionally, a Kappa test can be performed pre-collision, by comparingthe velocities of the conditioned feature and the original Zyoton, i.e.,ω₁, and ω₂, respectively. As a conditioned feature is generallyconstructed to have only a fraction of the energy of the originalZyoton, ω₁ is typically only a fraction of ω₂. As such, in comparing ω₁with ω₂, either one or both of the velocities are scaled, and it istested whether the magnitude of a difference between the velocities,after scaling one or both, is less than a Kappa parameter κ_(DV2).

As described below in various embodiments, the modified Zyoton Z′_(i) isrenormalized to produce a renormalized Zyoton Z″_(i), having dispersionvelocity ω₄ that is comparable to the dispersion velocity ω₁ of theconditioned feature CF_(i). The energy of the renormalized Zyoton isalso expected to be comparable to that of the conditioned feature.Therefore, in some embodiments, Kappa test can be performed by comparingthe velocities of the renormalized Zyoton and the original Zyoton, i.e.,ω₄ and ω₂, respectively. Here again, as the renormalized Zyoton isexpected to have only a fraction of the energy of the original Zyoton,ω₄ is typically only a fraction of ω₂. As such, in comparing ω₄ with ω₂,either one or both of the velocities are scaled, and it is testedwhether the magnitude of a difference between the velocities, afterscaling one or both, is less than a Kappa parameter κ_(DV1). In someembodiments, κ_(DV1) can be the same as or approximately equal toκ_(DV2). In general, the difference in the velocities to be compared isan absolute difference, i.e., a magnitude of the difference regardlessof whether one velocity is greater than or less than the other iscompared with an applicable Kappa parameter.

As described above, co-dependency condition can be tested pre-collision,i.e., by testing whether |α_(T)*(ω₂)−(ω₁)| is less than a Kappadesignated κ_(DV2), where α_(T) is the scaling factor applied duringtesting to the velocity of the original Zyoton. As described above, thevelocities can be compared by scaling ω₁ instead of or in addition toscaling ω₂. In order to satisfy this test, a nominal scaling coefficientα_(C) is applied to achieve a pre-selected ratio (α_(Z)) of spectralenergy of Zyoton to the spectral energy of a conditioned feature. Theratio α_(Z) can be, e.g., 100; 500; 1,000; 2,000; 3,500, etc. In someembodiments, the spectral energies in determining the ratio are computedusing only a limited number (e.g., 2, 6, 8, 15, etc.) of frequencycomponents of the Zyoton and the conditioned feature. The nominalscaling coefficient α_(C) is applied to the original Zyoton or to theconditioned feature, or to both waveforms such that the pre-selectedratio (α_(Z)) of spectral energies of the Zyoton and the conditionedfeature are achieved.

The term nominal scaling coefficient is used because different featuresfrom the same or different spectra from the same or different media tobe analyzed are likely to result in somewhat different scalingcoefficients to establish the ratio α_(Z) of spectral energy of theZyoton to the spectral energy of the conditioned feature prior to thefirst collision. Generally, the following condition is imposed on theratios of the nominal scaling coefficient:

${{\frac{\left( {{\alpha\; C} - {\alpha\;{Fi\_ MAX}}} \right)}{\alpha\; C}} < 0.1},0.2,$or 0.5, and

${{\frac{\left( {{\alpha\; C} - {\alpha\;{Fi\_ MIN}}} \right)}{\alpha\; C}} < 0.1},$0.2, or 0.5, where α_(Fi) _(_) _(MIN), α_(Fi) _(_) _(MAX) respectivelydenote the maximum and minimum scaling coefficients encountered toachieve a desired spectral energy ratio α_(Z) (e.g., 1000) with an α_(C)(e.g., 0.001). The parameters α_(Fi) _(_) _(MIN) and α_(Fi) _(_) _(MAX)are any members of a set of all spectral energy scaling coefficients{α₁, α₂, . . . , α_(∝)} required in a collision computing sequence usedto analyze spectral features from a spectroscopically analyzed sample inthe frequency domain. It is to be understood that these coefficients{α₁, α₂, . . . , α_(∝)} and α_(Z) may be computed and applied in thetime domain or in the frequency domain, and are distinct from thecomputing-coefficient α described below in the discussion of thecollision operator.

Another important co-dependency condition is that the width of thepost-collision Zyoton waveform divergence be less than a presetthreshold τ. A width of a Zyoton waveform can be described as a time lagbetween any two phases of a Zyoton waveform, such as time lags t1, t2,and t3 depicted in FIG. 14A. After collision, one or more of thesewidths can change, as in t1′, t2′, or t3′ shown after a collision inFIG. 14B, but the second co-dependency condition requires that each ofthese differences, i.e., Δt1=t1′−t1, Δt2=t2′−t2, and Δt3=t3′−t3, be lessthan τ.

The selection of values for κ and τ are related to the collision grid,bandwidth of the Zyoton, and peak energy of the Zyoton. As the values ofκ and τ bound the post-collision spectral energy change that can occurto preserve Zyoton properties, they also bound the original spectralenergy of the colliding entity, i.e., the conditioned feature waveformfor the first collision by imposing a design constraint on the carrierkernel spectral energy. The number and specifics of frequency componentsand their amplitudes of the carrier kernel are thus constrained by κ andτ. An increase in the κ and τ values may allow for an increase in theamplitude(s) of the first k frequency components, as well as the numberk of analyte-information representing components that are used in thepre-collision and post-collision computations described below. Once κand τ are established, the properties of the optimized carrier kernelused for conditioning the features can be locked. Exemplary values forκ_(DV2) and τ for noninvasive glucose measurement are 0.6×10⁻⁶ and1.4×10⁻⁶, respectively, as determined, for example, by an L2 norm. Theparameters κ and τ are generally represented as unit-less numbers.

These conditions generally need to be met for every conditionedfeature-Zyoton pairing. If these two co-dependency conditions are notachieved, the collisions may not have computational utility or thecollision operator may become unstable. In various embodiments, thevariables κ_(DV1), κ_(DV2), κ_(DV3), and κ^(SYN) are used as tests ofcollision integrity before the first collision iteration as a limit ofthe difference in dispersion velocity (or spectral energy) between theZyoton and the conditioned waveform. Thereafter, before and/or after oneor more subsequent collision iterations, these variables can be used astests of collision integrity between the Zyoton and a modified Zyoton orbetween a Zyoton and a renormalized Zyoton. Optionally, these variablescan also be used to test a limit of the difference in dispersionvelocity (or spectral energy) between the Zyoton and the carrier kernel,when they are initially synthesized, in order to verify theircodependency. Upon completion of the conditioning process, eachconditioned feature can be represented in the computer memory as aparameterized waveform. One or more Zyotons and one or more conditionedfeatures are computationally collided in step 10 (FIG. 13).

Typically, the absorption energy loss due to the analyte is much lessthan that due to one or more confounders, and the total energy lossesdue to the analyte and confounders are significantly smaller than theloss due to scattering and/or dispersion of the radiation in the medium.As such, the signal-to-clutter ratio (SCR) of a signal corresponding tothe energy loss due to the analyte of interest to the overall energyloss due to confounders and scattering is often very low—e.g., as smallas 10⁻⁴ or 10⁻⁶. By tuning the Zyotons, the collision operator, one ormore parameters thereof, and the modulation of the feature to a requiredSCR increase, the energy loss represented by the feature can beamplified, without introducing noise or distortion, in one or morecollisions, and can then be measured.

One key objective of the Zyoton tuning process is to configure theZyoton such that energy loss estimated from a Zyoton collided with aspecific conditioned feature, after the one or more prescribed number ofcollision iterations, is strictly monotonic, that is, trending in thesame direction throughout the entire interval, as the concentration ofthe analyte in the sample over the analyte concentration range ofinterest, when the feature concentrations and computed energy loss arerepresented as ordered pairs. It is to be understood that the termmonotonic, while used here in the sense of a constantly increasing trendof a data set in which the analyte concentrations are constantlyincreasing, can also be used to describe the constantly decreasing trendof a data set in which the analyte concentrations are constantlydecreasing. The collision process can be thus described as a monotonictransformation of an acquired spectroscopic dataset. A calibration tableand/or curve can be used to determine concentration of the analyte inthe medium according to the amplified energy loss or change, asrepresented by the final result of one or more collision iterationsyielding a monotonic response.

In various embodiments, several collision iterations are used to expandthe dynamic range of the estimated spectral energy changes so thatgreater precision can be obtained during the post-collision projectionprocess for predicting analyte concentration. Specifically, in variousembodiments, the collision process is iterative in which the firstcollision iteration in a collision sequence is between a Zyoton and aconditioned feature. Subsequent collision iterations may be between therenormalized output of the preceding collision (i.e., a renormalizedZyoton) and the same or a different Zyoton. Whenever more than onecollision iteration is used (i.e., the number of iterations

>1), the colliding entities are usually a renormalized Zyoton and theoriginal Zyoton or a new Zyoton.

Different Zyotons may be used to collide with different conditionedfeatures. Different features extracted from varying regions of theoriginal source data can have vastly varying differences in theirmeasurement scale, sometimes varying over several orders of magnitude.With such variations, in some embodiments, the co-dependency conditioncannot be achieved using the same Zyoton for all selected spectralfeatures. Thus, different Zyotons are designed and tested to ensure thateach conditioned feature and Zyoton pair satisfies the codependencycondition described above.

The analyte in the medium to be analyzed generally induces a change inthe measured parameters of the medium (such as absorption or emission ofenergy) relative to those parameters if no analyte were present in themedium. This change is represented in the acquired spectral data of themedium and, hence, in one or more extracted features. The Zyotons, theconditioning of the features, and the collision operator are designedsuch that one or more collisions in step 10 (FIG. 13) generally induce ameasurable change in one or more properties (e.g., spectral energyreduction due to incident light absorption by the analyte in themeasured spectral bandwidth) of the waveform resulting from thecollisions. In step 12 (FIG. 13), after a preset number of collisionsbetween a conditioned feature and the corresponding Zyoton have beencompleted, such change in the resulting waveform is computed todetermine the net spectral energy gain or loss for each collidedfeature. In some embodiments, the process is configured to berepresented as an energy gain, but represents a loss in spectral energydue to absorption of energy by the analyte.

Following a collision process involving one or more collisioniterations, the changes in the properties of the post-collision waveform(the modified Zyoton) before and after the collisions may be analyzed asa mechanism to infer properties of the feature. Impacted properties mayinclude changes in propagation velocity, peak energy, dispersionvelocity, and changes in the spectral envelope. These changes can bequantified through changes in the spectral energy of the modified Zyotongenerated after each collision relative to the spectral energy of theoriginal Zyoton. In the first iteration, at least a portion of theenergy of the feature that is represented by the conditioned feature istransferred to the modified Zyoton and then to the renormalized Zyoton.In subsequent collision iterations, the energy of the feature istransitively transferred from a renormalized Zyoton generated in aprevious iteration to a renormalized Zyoton generated in the currentiteration.

In effect, the collision computing process examines how the energy fromthe incoming, uncharacterized feature interacts with the properties ofthe stable Zyoton waveform to produce a post-collision waveform with theanalyte information content of the original feature. Depending on howthe conditioned feature waveform itself has been influenced by theunderlying analyte concentration, and by confounders and the media, itsinteraction with the Zyoton can be different. As such, a Zyoton can bedescribed as a nonlinear amplifier system and a feature as aperturbation. The repeated collision process is thus a protocol forcharacterizing analyte properties and estimating concentration in theuncharacterized samples.

The absorbed spectral energy, represented as a net gain in the energy ofa modified Zyoton relative to the energy of the original Zyoton, istransformed into an analyte concentration using a projection operator.Projection is a generalized process of representing the averageestimated post-collision spectral energy absorption in terms of net,renormalized spectral energy changes corresponding to an uncharacterizedsample, and associating these net energy changes with thosecorresponding to known, analyte levels (represented in a “referencesystem”), as described below in detail. The reference system may or maynot have any physical relationship with the samples being analyzed. Forexample, in non-invasive glucose measurement, as described below, thereference system may be a collection of tissue simulating dispersiveliquid or gel samples (also referred to as “phantoms” or “tissuephantoms”), and containing specified glucose concentrations. Theprojection operator can relate the observed spectral energy absorbed inspectra from uncharacterized human subjects to known concentrations ofglucose in an Intralipid fat emulsion or gel-based tissue phantomsystem. To this end, calibration curves can be used to relate the twodisparate systems. As a generalized mechanism, projection can beaccomplished by mapping or transforming the computed post-collisionspectral energy absorption to an absolute reference system of knownconcentrations. Projection may optionally involve transforming theestimated spectral energy change (gain or loss) through one or moreintermediate systems through the use of calibration curves prior toprojecting the spectral energy change onto the reference system.

Collision Computing Process

With reference to FIG. 15, in various embodiments, collision computingis performed for selected features, sequentially or in parallel.Features may be conditioned and introduced into the collision computeras one-dimensional vector data objects including one or more numericalvector elements. Prior to introduction into the collision computer atstep 4, the complete spectrum (or other data set) may be preprocessedand standardized. The features are transformed at step 6 into a spectralwaveform using a form of frequency modulation called the conditioningprocess.

An optional preprocessing performed on feature data involves numericalscaling of the feature data amplitude vector with respect to anotherreference data vector. The reference data vector can be derived from anin-line, in-measurement property used to compensate for variability inthe measurement. This may be done in systems where there is highmeasurement-to-measurement variability during the acquisition of featuredata (such as when the acquisition involves the detection of NIR lightdiffusely reflected from tissue). During preprocessing, the raw sensordata can be transformed into a data representation that is appropriatefor the follow-on conditioning and collision computing processes. As anexample, the acquired raw sensor data could be in the form of discretecounts, current, voltage or some form of flux intensity, with valuesranging from a minimum to a maximum as defined by the sensor's dynamicrange. The sensor or data acquisition platform may be optionallyequipped with a hardware reference channel that can simultaneouslycollect raw reference data, also in the form of discrete counts,current, voltage or some form of flux intensity under a fixed condition(such as dark current or when there is no sample exposed to the sensor).The preprocessing step can combine sensor data and its referencecounterpart to create a data object (“absorbance” or“pseudo-absorbance,” as described below) that can be used in subsequentcomputation. One example is the preprocessing of diffusely reflectedspectral intensity amplitudes by combining them with referenceamplitudes to transform the intensity data into absorbance ortransmittance representations in spectroscopic analysis.

The standardization step can involve computations that are implementedto further transform the preprocessed data to remove the effects ofsensor to sensor variability, variability due to data formats andvariability due to hardware changes or degradation. Standardizationgenerally helps to ensure syntactic integrity and can enhance semanticequivalence of the data, irrespective of differences in the hardwarethat was used to collect it. Both preprocessing and modulation aredescribed in detail below.

An optional frequency modulation may be performed as part of the sensordata conditioning process at step 6. This frequency modulation step,referred to as an optional “precursor frequency modulation,” has adifferent purpose compared to preprocessing and standardization. Indealing with sensor measurements to observe materials where interferencefrom clutter is high (SCR<<1), frequency modulation may be used as amechanism to expand the observability state space, i.e., observablestates from which the properties of the material (e.g., an analyte) canbe classified, quantified, or inferred. By coupling the sensor datafeatures or preprocessed, standardized sensor data features withcarriers of different frequencies in a precursor modulation, the statespace over which the data are analyzed can be transformed so as toincrease the probability of detection of the amount, event, material orproperty of material of interest. Unlike the conventional frequencymodulation in signal processing where a carrier wave is used to encodethe signal or information by varying the instantaneous frequency of thewave, the precursor modulation can increase the observability space ofevents and materials.

The conditioned feature is then introduced into the collision computerat step 4, along with a complementary entity—the collision waveform orZyoton, generated at step 8 using the criteria described above. Thesynthesis of the Zyoton and the carrier kernel used to generate theconditioned feature is also described below. Within the collisioncomputer, the conditioned feature waveform and Zyoton waveforms arerepresented as waveforms propagating toward each other on a collisiongrid. During the collision at step 4, the conditioned feature wavefrontcollides and couples with the Zyoton wavefront, thereby changing theproperties of the Zyoton and producing a resulting waveform called amodified Zyoton. The Zyoton and the feature waveforms are fed into thecollision computer that performs bracketed interactions between the twopropagating waveforms and, in particular, the colliding wavefronts,producing the new post-collision waveform i.e., the modified Zyotonwaveform. Unlike conventional modulation techniques, which typicallyinvolve multiplication and/or convolution operations, the bracketedinteraction operator involves conditional operations and isnon-invertible.

The amplitudes of the Zyoton and/or the conditioned feature may beoptionally modified prior to the collision thereof, e.g., to ensure theco-dependency conditions described above, and the Zyoton and/orconditioned feature components may be optionally shifted and alignedprior to the collision thereof. Phase modulation may be applied to themodified Zyoton. The collision operation is controlled, as describedbelow, such that a measureable change occurs in a property (e.g.,spectral energy) of the modified Zyoton relative to the correspondingproperty of the original Zyoton, and the change is attributable to thecorresponding property of the feature, as represented by the conditionedfeature. To this end, various collision operators such as shifting,scaling, phase rotation, number of iterations, etc., can be determinedat step 12 based on the properties of the medium to be analyzed, theanalyte, the sensor, and the computing system.

In various embodiments, the conditioned feature waveform may be unusedafter the first collision at step 10. A second collision may occur, atstep 4, between the post-collision modified waveform followingrenormalization thereof (called the renormalized Zyoton), and theoriginal Zyoton or a different Zyoton. The different Zyoton, in general,is selected such that it is co-dependent, as described above, with therenormalized Zyoton. Similarly, additional collisions can be performedbetween the waveform resulting from the previous collision, afterrenormalization thereof, and the original Zyoton or a different Zyoton.

In generalized collisions, one of three additional collision modalitiescan be implemented: (i) successive collisions between the originalconditioned feature and the post-collision modified and renormalizedZyoton waveform from the preceding collision; (ii) successive collisionsbetween the original conditioned feature with a new Zyoton waveform; and(iii) successive collisions between the post-collision modified andrenormalized waveform from the previous collision and a new Zyotonwaveform. Whenever successive collisions are described, arenormalization process described below is generally included as anintegral part of the iterative collision process. The renormalization,in general, includes energy scaling and/or removal of one or morefrequency components, and redistribution of the energy of the removedcomponent(s). When a modified Zyoton is renormalized and collided withthe original Zyoton in a subsequent iteration, the energy scaling thatis applied can be different from the energy scaling applied when themodified Zyoton is renormalized and collided with the originalconditioned feature.

The measurable changes in post-collision waveform properties relative tothe corresponding property of the original Zyoton, e.g., the net gain inspectral energy of the coupled waveform (i.e., the modified Zyotonand/or the renormalized Zyoton), as computed using the differencebetween the spectral energy of the Zyoton waveform and post-collisionmodified and renormalized Zyoton waveform following one or morecollisions, can be used to estimate the presence and concentration of ananalyte in a medium.

An example illustrating the utility of this technique is thenon-invasive estimation of glucose (an analyte of interest) in humanskin tissue, using optical diffuse reflectance spectroscopy, whereby theconcentration of glucose can be determined based on the measurement ofselective spectral absorption of energy when skin is illuminated withnear-infrared radiation. The analyte concentration can be determined bycomputing the spectral energy distribution of the post-collision Zyotonwaveforms after all collision iterations are completed. The spectralenergy gain between the energies of the modified Zyoton obtained afterthe last iteration and the original Zyoton, as represented by thespectral energy of the last renormalized Zyoton, is related to thefeature properties as represented by the conditioned feature waveformproperties. The collision process is used to estimate how much of theloss of energy of the incident NIR in the original feature waveform isdue to the presence and concentration of the analyte. In a properlyselected and designed Zyoton, carrier kernel, and collision operation,an ultra-small net energy loss due to absorption by the analyte can bedetected and amplified on a dynamic range that extends to as much asfourteen orders of magnitude, using Zyotons with frequency bandwidths inthe MHz region.

One embodiment, used for a non-invasive analyte measurement, employs20,000 repeated collisions to estimate the net energy gain due toabsorption at the feature level and to overcome the high level ofinterference from confounders. In some embodiments, the collisionoperator may be modified at step 16, if required, and then the result isre-introduced into the collision computer at step 4, for the nextcollision at step 10. In some embodiments, the collision operator is notmodified between one or more or all of the subsequent collisioniterations. The process is repeated until the required number ofcollisions are completed, as determined at step 14, and the results maybe output (reported) and/or may flow at step 20 to the next step forestimating the net energy loss due to absorption.

Post-Collision Renormalization

With reference to FIG. 16, the spectral energy of a post-collisionresult (e.g., a Zyoton perturbed by a conditioned feature) is computedat step 6 to estimate the change due to the presence and concentrationof material exhibited in the spatial, temporal, or spectral windowdefined by the feature. For systems with several collision iterations,the output after each collision is generally renormalized in steps 8,10, and 12 before a subsequent collision can occur.

This renormalization is performed for two reasons: (i) removal of theenergy of the original Zyoton, and (ii) redistribution of energy lost bya truncation operation. All collisions following the first collision maybe between a Zyoton and a renormalized, modified Zyoton resulting fromthe preceding collision interaction, so the original spectral energy ofthe Zyoton needs to be removed from the modified Zyoton prior to thenext collision by properly scaling the frequency domain amplitudes ofthe analyte-information representing (e.g., the first k) frequencycomponents.

In statistical field theory and quantum field theory, the pileup ofcontributions from a large number of measurement scales involved in ameasurement problem can lead to intractability of measurements. Arenormalization of the measurement scales can address the intractabilityassociated with a large number of measurement dimensions in problemsolving, as described in K. G. Wilson, “The renormalization group:critical phenomena and the Kondo problem,” Reviews in Modern Physics,47, 4, 773 (1975). The collision computing process does not generallyinvolve analysis of direct measurements of an analyte at differentmeasurement scales and, as such, unlike the renormalization employed instatistical fields theory and quantum fields theory, the renormalizationdescribed herein is directed to readjustment of the observable, e.g.,the spectral energy, across successive iterations.

In general, collision computing also transforms signal detection andquantitation to a spatio-temporal (space-time) framework, which allowswaveform interactions which may not be fully accounted for or modeled,and may include approximations used for numerical stability incomputation. The term framework is used here as the space-time scale forimplementing collisions and may not be related to the space-timedimension associated with acquiring the data. The framework can be acomputational framework, or it may be related to the apparatus forimplementing a collision computer such as a digital computer, graphicprocessing unit processor, or optical computer, or any such examplesimplemented in firmware.

The result of every collision interaction is baselined observable energyscalar i.e., the spectral energy gain of the modified Zyoton relative tothe spectral energy of the original Zyoton as estimated from a fixedsubset of frequency components. The spectral energy of the originalZyoton selected from a database 1, and used in the collision, isdetermined at step 2. That spectral energy is used in step 8 todetermine a normalization coefficient, so that the energy of theoriginal Zyoton can be removed from the modified Zyoton at step 10.

As described above, the second objective of the renormalization istruncation of the modified Zyoton, so that the renormalized Zyoton canbe effectively collided again with the original Zyoton, or with anotherZyoton. New frequency components can be created in the transition andnon-analyte information representing bands during a collision iteration.The introduction of these components may cause a change in dispersionvelocity and/or divergence, so that the co-dependency condition may notbe satisfied for the next collision iteration. As such, one or more ofthese components may be removed during truncation of the modifiedZyoton. In general, subportion(s) of the non-analyte informationrepresenting and/or transition portions (these terms are describedbelow) of the modified Zyoton are removed, and the energy thereof isredistributed among the surviving subportions. This energyredistribution can be achieved via amplitude balancing at step 12. Ifrenormalization is implemented in the frequency domain, the amplitudebalancing can compensate for the impact of any removal of one or morefrequency components of any entity participating in a collision.

The truncation generally results in a loss of spectral energy of themodified Zyoton. The energies of the removed frequency components of themodified Zyoton are computed and re-distributed across the survivingfrequency components of the modified Zyoton. This is implemented usingan amplitude balancing operation at step 8. Specifically, in thefrequency domain, the amplitude re-balancing (or re-distribution)operation entails distribution of the removed spectral energycontribution from the removed frequency components over the remaining mand j frequency components of the modified Zyoton. Thus, the frequencydomain amplitudes of the surviving m and j components are adjusted atstep 8 during the renormalization process.

Alternatively or in addition, renormalization may further include anadditional truncation of the modified Zyoton to select the lengththereof. To this end, relatively smaller-amplitude frequency componentsof the modified Zyoton may be removed to ensure that thefrequency-domain length of the renormalized Zyoton waveform matches thefrequency-domain length of the original Zyoton and/or a new Zyoton withwhich the renormalized Zyoton is to be collided. This truncation mayalso be followed by an additional amplitude balancing operation in step12, in which the amplitudes of all the remaining m and j frequencycomponents of the truncated modified Zyoton are adjusted to compensatefor the energy of the frequency components removed in the additional oralternative truncation process. This renormalized post-collision Zyotonwaveform may then be reused in the next collision iteration as describedwith reference to FIG. 15. Renormalization can be implemented in thetime domain by modifying the time-domain velocity and/or dispersionvelocity of the modified Zyoton.

In general, the renormalization of the post-collision waveform of themodified Zyoton allows removal therefrom of the energy contained in theoriginal Zyoton after each collision iteration so that energy changescan be successfully accumulated in a multi-collision protocol forquantifying analyte presence and concentration. In some embodiments, tworenormalization parameters are derived using spectra generated from amodel of waveform propagation over a collision grid. The firstrenormalization parameter includes a set of numbers associated with therespective amplitudes of every frequency-domain component of thewaveform, matched to the length of the truncated (e.g. down-sampled)result after collision. The first renormalization parameter modifies thefrequency domain amplitudes of the surviving frequency components, suchthat the spectral energy of all frequency components of the modifiedZyoton, ignoring the first k analyte-information representingcomponents, is the same as the spectral energy of all but the first kfrequency components of the conditioned feature used in the collision.This can be tested by comparing the spectral energy of all but the firstk components of the renormalized Zyoton with the spectral energy of allbut the first k components of the conditioned feature.

The renormalization process also computes a second parameter, i.e., arenormalizing scaling factor, which changes the frequency domainamplitudes of the first k components to provide the next waveform forthe next collision. The renormalizing scaling factor is designed suchthat, the frequency domain amplitudes of the first k frequencycomponents of the renormalized modified Zyoton are within 0.1%, 1%, 5%,10%, 20%, 30%, or 50%, 100%, etc., of the frequency domain amplitudes ofthe first k frequency components of the conditioned feature. As aresult, the energy of the renormalized modified Zyoton becomessubstantially similar to that of the conditioned feature just prior tocollision and is within 0.1%, 0.4%, 1%, 2%, 5%, or 10%, etc. of theenergy of the conditioned feature. This can also ensure that the Kappatest of co-dependency condition is satisfied for the next collisioniteration. In some embodiments, this computation is done up to thefifteenth decimal digit for high precision and to accommodate SCR below0.0001. In some embodiments that employ only a single iteration of acollision operation, if renormalization is performed, the frequencydomain amplitudes of the first k frequency components of therenormalized modified Zyoton are adjusted such that the resulting energyof these k components can be up to two or three orders of magnitude ofthe energy of the corresponding frequency components of the conditionedfeature to expand the dynamic range of energy change. Applications whereonly one collision iteration is used in conjunction with renormalizationinclude classification of analyte levels into 3, 5, 7, 12 etc., bands orregions.

The renormalization process allows accumulation of energy changesgenerally only due to absorption of energy by the analyte in eachfeature. The purpose is to transform all the energy changes to arelative scale and dynamic range which can then be projected ontoanalyte concentrations using a dataset that providesconcentration-specific references. FIG. 17 shows the morphologicalenvelope of an exemplary Zyoton and conditioned feature used incollision computing. FIG. 18 shows the Zyoton and the conditionedfeature waveform on a “spatio-temporal” grid and the Zyoton waveformbefore a collision. FIG. 19 illustrates the progression of a collisionbetween the conditioned feature and the Zyoton wavefronts during acollision. FIG. 20 shows the modified Zyoton after the collision. FIG.21 shows the modified and renormalized Zyoton after the collision andpreceding the next collision in a multi-iteration collision protocol.FIG. 22 shows the modified and renormalized Zyoton after a finite numberof

collisions in a multi-iteration collision protocol. FIG. 23 shows atypical energy gain trajectory due to the net spectral energy changeresulting from analyte-specific absorption evolving over severalcollision iterations in a collision computer for two features drawn fromsamples with two different material concentrations (for example, tissueglucose). The two curves show the amplification resulting from collisioncomputing.

With reference to FIGS. 24-27, the collision and renormalizationprocesses are illustrated schematically in the time domain. FIG. 24illustrates a collision between a Zyoton Z_(i) 1 schematicallyrepresented by a bell-shaped envelope and a conditioned feature γ(FWi)8. In the time domain, a Zyoton typically includes several peaks such asthose shown in FIG. 12A, which, together, can be representedschematically by an envelope such as that shown in FIG. 24. Each Zyotonpeak itself can be a schematic envelope, i.e., each peak can be a groupof one or more peaks, as shown in FIG. 12B. The conditioned feature mayinitially have length

′ in the time domain, while the zyoton has length

in the time domain. The length of the conditioned feature 6 is adjusted,e.g., by interpolation, down-sampling, and/or truncation, to match thelength

of the Zyoton to allow the collision therebetween. The result of thefirst collision is shown in FIG. 25 as a modified Zyoton envelope 14,Ω(γ(FW_(i)),Z_(i))t₁. The energy of the modified Zyoton is E₁, theenergy of the original Zyoton is E₀, and the energy gain (E₁−E₀) orloss, where (E₁−E₀) is less than zero, is proportional to ΔE, i.e., isthe energy of the analyte-information representing portion of theconditioned feature FWi. FIG. 25 shows that the modified Zyoton withenergy E₁ still has length

. In some instances, however, the length of the modified Zyoton can bedifferent from

, e.g., the length can be

″.

In FIG. 26, the modified Zyoton Ω(γ(FW_(i)),Z_(i))t₁ is renormalized toa renormalized Zyoton N(Ω₁), 20. The renormalization includes removal ofthe energy of the original Zyoton and redistribution of the portion ofthe modified Zyoton removed by truncation. The energy of theanalyte-information representing portion of the renormalized Zyoton isΔE₁. The renormalized Zyoton N(Ω₁), 20 is collided again with theoriginal Zyoton Z_(i), to yield the new modified Zyoton shown in FIG. 27as Ω(N(Ω_(i)),Zi)t₂, 22, having energy E₂. The energy gain of the newmodified Zyoton relative to the original Zyoton, i.e. (E₂−E₀) isproportional to the energy ΔE₁ of the analyte-information representingportion of the renormalized Zyoton N(Ω₁), which is proportional to theenergy ΔE of the analyte-information representing portion of theconditioned feature.

In each subsequent collision iteration, the energy gain of the modifiedZyoton generated in that iteration relative to the energy of theoriginal Zyoton, represented by (E_(n)−E₀) for the n-th collisioniteration, is proportional to the energy of the analyte-informationrepresenting portion of the renormalized Zyoton generated in theprevious collision iteration, i.e., ΔE_(i), which itself is transitivelyproportional to the energy ΔE of the analyte-information representingportion of the conditioned feature.

Features, Collision, Renormalization, and Energies

In FIG. 9, E_(I) represents the spectral energy of the radiationincident upon a medium, in a wavelength band [λ¹ ₁, λ¹ ₂]. Forsimplicity, E_(I) is assumed to be constant across all wavelength bandsand, as such, the spectral energy of the incident radiation (e.g., inthe near infra-red region of the electromagnetic spectrum) in anotherwavelength band [λ² ₁, λ² ₂] is also E_(I). In the medium (e.g., aportion of skin), a portion of the incident radiation is absorbed by oneor more confounders. That portion can be less than 1%, 2%, 5%, 10%, etc.A portion of the incident radiation, e.g., less than 0.1%, 0.2%, 0.6%,1%, 1.5%, 3%, 7%, etc., may be absorbed by an analyte of interest, andis denoted by E_(A). In some instances (e.g., in tissue measurement), anadditional portion of the radiation may be scattered within the tissueand lost, and is considered to be the lost portion E_(L). A portion ofthe incident radiation is not absorbed by the analyte, any confounders,or otherwise lost (e.g., due to scattering) present in the medium, andis reflected from (or passes through) the medium. The reflectedradiation can be detected by a detector.

The analyte of interest may absorb radiation at some wavelengths and maynot absorb the radiation, at least at a significant level, at some otherwavelengths. For example, in FIG. 9 it is assumed that the analyteabsorbs radiation in the wavelength band [λ¹ ₁, λ¹ ₂], designated asAnalyte Feature F1, and that the analyte does not substantially absorbradiation in the wavelength band [λ² ₁, λ² ₂], designated as Non-AnalyteFeature F2. For the Analyte Feature F1, the energy absorbed by theanalyte is E_(A1), the energy absorbed by one or more confounders isE_(C1), energy lost (i.e., absorbed by elements of the medium other thanthe confounders and the analyte) is E_(L1), and energy reflected by themedium and detected by the detector (denoted E_(O1)) is E_(R1). For theNon-Analyte Feature F2, the energy absorbed by the analyte is E_(A2)(which could be a negligible amount), the energy absorbed by one or moreconfounders is E_(C2), energy lost is E_(L2), and the energy reflectedby the medium and detected by the detector (denoted E_(O2)) is E_(R2).Therefore:ΔE ₁ =E _(I) −E _(O1) =E _(L1) +E _(C1) +E _(A1);ΔE ₂ =E _(I) −E _(O2) =E _(L2) +E _(C2) +E _(A2) =E _(L2) +E_(C2),because E _(A2)≃0; andΔE ₁ −ΔE ₂=(E _(L1) −E _(L2))+(E _(C1) −E _(C2))+E _(A1)In the equations above, E_(I) is known, and E_(O) values can be obtainedby direct measurement from the detector. E_(L), E_(C), and E_(A), areunknowns for each feature.

The spectral energy of feature F1 is represented byΔE₁=(E_(L1)+E_(C1)+E_(A1)). The spectral energy of a conditioned featureis also represented by ΔE₁=(E_(L1)+E_(C1)+E_(A1)). The Zyoton and thecollision operator are designed such that after the first collisionbetween the Zyoton and conditioned feature, the energy of the modifiedZyoton (E_(Z) ¹) changes relative to the energy of the original Zyoton(E_(Z) ⁰), but the change corresponds, in substance, only to E_(C1) orE_(A1), and not as much to E_(L1). In this way, E_(C1) and/or E_(A1) canbe extracted, even though E_(L1) is unknown.

In both ΔE₁ and ΔE₂, typically, E_(L)>>E_(C)>E_(A). As such, if ΔE₁ andΔE₂ are amplified using a conventional nonlinear amplifier, in thedifference between amplified ΔE₁ and amplified ΔE₂, the differencebetween E_(L) would dominate. Collision computing can selectivelyamplify E_(C1) and/or E_(A1) and not E_(L), so that the differencebetween ΔE₁ and ΔE₂ can be used to determine the energy absorbed by theanalyte, which in turn can be used to determine accurately the analyteconcentration.

Referring to FIG. 10A, in one embodiment, radiation of energy E_(I) isdirected to a medium and the radiation reflected by the medium isdetected at a detector. An absorbance spectrum “O,” representing E_(O)across a range of wavelengths, is derived from the detected radiation.Waveforms L, C¹, C², and A represent, respectively, the absorbancespectra corresponding to the radiation lost (representing E_(L)), theradiation absorbed by a confounder C¹ (representing E_(C) ¹), theradiation absorbed by a confounder C² (representing E_(C) ²), and theradiation absorbed by the analyte A (representing E_(A)). In general,the properties of the medium, which may determine the radiation that islost, the concentrations of the confounders C¹ and C², and theconcentration of the analyte are not known. As such, the absorbancespectra L, C¹, C², and A are also not known. These absorbance spectra,however, are the components of the absorbance spectrum O, which can bederived from the radiation detected at the detector. In FIG. 10A,spectra corresponding to two confounders are shown for illustration. Ingeneral, a medium may include no confounders, only one confounder, ormore than two (e.g., 3, 5, 8, etc.) confounders.

The observed spectrum O is divided into several (e.g., 2, 4, 5, 10, 15,18, 24, 32, 50, etc.) regions called features. With reference to FIG.10B, a feature F₁ includes a region O₁ of the observed absorbancespectrum O. Feature 1 also includes regions L₁, C¹ ₁, C² ₁, and A₁ ofthe absorbance spectra L, C¹, C², and A, respectively. Here again, thespectrum O₁ includes the spectra L₁, C¹ ₁, C² ₁, and A₁, but theseindividual spectra are not known. The spectrum L₁ represents E_(L1);spectrum C₁ ¹ represents E_(C) ₁ ₁; spectrum C² ₁, represents E_(C) ₂ ₁;and spectrum A₁ represents E_(A1). FIG. 9 also depicts the energyabsorbed by one or more confounders as E_(C1). In general, for Nconfounders, the absorption is additive and can be expressed asE_(C1)=Σ_(i=1) ^(N) E_(C) _(i) ₁, where N≧0. This additive absorption isnon-invertible and components E_(C) _(i) ₁ generally cannot beaccurately recovered using a linear transformation, spectraldeconvolution, or other passive signal processing technique.

Although the actual spectra L₁, C¹ ₁, C² ₁, and A₁ are not known, fromspectroscopic analysis of the analyte alone (in the solid or liquidphase or in solution), also referred to as a “pure component spectrum,”certain parameters of features from these spectra, called spectralparameters (such as the amplitude envelope or spatial frequencydistribution obtained by computing a Fourier transform of a featurevector), can be determined. Pure component spectra represent theabsorbance-wavelength relationship for the analyte of interest and/orfor one or more confounders.

A carrier kernel, with at least an order of magnitude higher spatialfrequency compared to the frequencies associated with Fouriertransformed feature F1, is modulated using the waveform O₁ that iscalled a feature waveform and that represents the feature F₁. As anexample, a system with an expected concentration range of about threeorders of magnitude could require a five-to-six order of magnitude rangein post-collision spectral energies, and a carrier kernel with a 1 MHzto 100 MHz bandwidth would generally be suitable. The various spectralparameters are used to select one or more parameters of the carrierkernel and/or one or more parameters of the modulation. The desiredtarget dynamic range of post-collision spectral energies and precisiondesired for the measurement determine the fundamental frequencies andnumber of frequency components of the carrier kernel, collectivelycalled modulation parameters. The modulation of the carrier kernel bythe feature waveform O₁ yields a modulated waveform called a conditionedfeature.

In general, a conditioned feature includes several components, each ofwhich is associated with a different spatial frequency. The modulationparameters are selected such that different frequency componentcombinations of the conditioned feature represent different spectralenergies associated with the feature. For example, with reference toFIG. 10C, in the conditioned feature F₁, some frequency componentsrepresent E_(C) ₂ ₁, i.e., the energy absorbed by the confounder C² atthe wavelengths defining the feature F₁. Similarly, some frequencycomponents represent E_(C) ₁ ₁; some frequency components representE_(A1); and some frequency components represent E_(L1).

With reference to FIG. 10D, in some instances, the frequency componentsrepresenting the energy absorbed by the analyte and the energycomponents representing the energy absorbed by one or more confounders(e.g., confounders 1 through N1 of a total of N confounders, whereN1≦N), overlap. Some other frequency components, such as E_(C) ^(Ni+1),represent the energy absorbed by the confounders (N1+1) through N, andyet other frequency components represent the lost energy. With referenceto FIG. 10E, the frequency components (some of which are fundamentalfrequencies and some of which are harmonics of those fundamentalfrequencies) representing the lost energy may overlap with the frequencycomponents representing the energy absorbed by one or more confounders,e.g., confounders N2 through N of a total of N confounders, where N2≧1.The term frequency components is used here to describe the sinusoidalspatial frequency components that make up a waveform. Such waveformsresult from “adding” together the series of sine wave frequencies thatwould result from a Fourier transform of the waveform. Thus, whateverits shape, a complex waveform can be split up into its individualspatial frequency components.

The representation of a particular energy (e.g., E_(C) ₁ ₁, E_(A1), acombination thereof, or E_(L1)), is a function of: (i) the number offrequency components representing that particular energy in themodulated waveform (i.e., the conditioned feature); (ii) the frequenciesof those frequency components; and (iii) the amplitudes of thosefrequency components. In general, for the j-th feature (denoted F_(j)),the relationship between the frequency components and their respectivecontribution to an energy such as E_(C) _(i) _(j), E_(Aj), E_(Lj), wherei denotes the i-th confounder, is not known. If it were known, a simpleFourier analysis of the conditioned feature would suffice to reveal thevarious energies of interest including E_(Aj).

The parameters of a Zyoton with which the conditioned feature iscollided and the parameters of the collision operator are also selectedusing the spectral parameters, i.e., the parameters derived from purecomponent analysis based on published or experimentally measured purecomponent spectra. If published spectra are used, knowledge about thenoise of the measurement system and the sources of the noise can beused. The frequency bandwidth and amplitude envelope of the b Zyotonsideband peaks shown in FIG. 12C depend on the morphological profile(e.g., the frequency spectrum of the second derivative of the waveform)of the pure component absorption spectrum waveform features. FIGS. 28Aand 28B show the pure component absorbance spectra for the analyte andone confounder of interest: glucose and collagen, respectively. FIGS.29A and 29B show the first derivative of pure component absorbancespectra for the analyte and one confounder of interest: glucose andcollagen respectively. FIGS. 30A and 30B show the second derivative ofpure component absorbance spectra for the analyte and one confounder ofinterest: glucose and collagen respectively, computed from the result ofFIGS. 29A and 29B.

As can be seen from FIGS. 30A and 30B, the two second derivative graphsfor the two compounds have different characteristics. The frequencycomponents and bandwidth of the pure component spectra and/or the first,second, or higher-order derivatives thereof, obtained by taking aFourier transform of the selected waveform and by determining the rangeof the frequency components in the Fourier transform, can be used indetermining the Zyoton frequencies and carrier kernel frequencies forconditioning the feature data, as described below.

In the example of glucose, the second derivative of a spectrum such asFIG. 30A, after optional interpolation by an amount of about 2¹⁰ to 2¹⁶,is added to random noise with a root mean square (rms) amplitude of therandom noise set to be 1000 times the rms amplitude of the secondderivative, to yield a combined second derivative waveform. In oneembodiment, the random white noise used is a colored grey noise with aC-weighting and correlation time of 10⁻⁶ seconds, but other weightingsand/or correlation times could also be used. In the preceding condition,the rms amplitude of the second derivative of the analyte is calculatedby taking the square root of the sum of the squares of the instantaneousamplitude values of the second derivative (amplitude as a function ofwavelength) over a window size that is twice the length of a feature inthe time domain.

The frequency bandwidth of the resulting combined waveform (noise+thesecond derivative of the interpolated data vector) and the relationshipamong the frequency component amplitudes over the wavelength regioncorresponding to the features are used to establish the bandwidth andfrequency components of the carrier kernel, as described below. Thus,the Zyoton and carrier kernel frequencies are related to the frequencycomponents of the analyte pure component spectrum or the first, second,or higher-order derivatives thereof, with added noise.

Specifically, as Zyotons are derived from inherently stable waveforms,the chromatic dispersion of the Zyoton waveform, the peak power, and thepulse energy in its first k-peak-power sorted frequency components(where k may be ≦6), may collectively control the limit of detection andquantitation that can be achieved in one or more collisions. Therefore,in some embodiments, Zyoton waveforms are generated that are solitonbased and show analyte-specific absorption effects more strongly inchanges in the spectral energy of the first k frequency components andscattering effects more strongly in changes in the spectral energy ofthe j frequency components. As mentioned previously, the total set offrequency components for the Zyoton is defined as H=k+m+j where k>0, m≧0and j>0, and the k and j frequency components, i.e., theanalyte-information representing and non-analyte informationrepresenting components do not overlap.

Once the number of frequency components that can yield an estimate foranalyte-specific absorption with the desired performance parameters(e.g., accuracy, precision, dynamic range) is established (e.g., 6 inone embodiment for non-invasive glucose measurement), the parameters ofthe collision grid, e.g., the bracket length in terms of numbers offrequency components of both the conditioned feature or renormalizedZyoton, as described below, grid spacing for propagation of the Zyotonwaveform, a window length, etc., are computed. In various embodiments,the window length specifies a total number of points (in the timedomain) or a total number of components (in the frequency domain) of theoriginal Zyoton, conditioned feature, and/or renormalized Zyoton thatare used in the collision operation. Examples of these parameters for anoninvasive glucose measurement are a window length of 2048 and a gridspacing of 10⁻⁶ seconds. The grid spacing can be additionally based oncharacteristic of the computing system, e.g., available numerical rangeand precision, available processing capacity and time, etc.

The window length for the collisions is generally set such that at leastthose frequency components of a conditioned feature (and a renormalizedZyoton) that are used in the computation of spectral energy change dueto analyte-specific collision interactions can be propagated. Changes inthe spectral energy of acquired features due to scattering losses may beintentionally filtered out from the post-collision spectral energycomputations through the use and choice of the window length that issmaller than the length of all of the data object containing thefrequency components of the Zyoton waveform.

Limiting the collision window length can thus reject incorporation ofscattering-related spectral energy changes by filtering out thenon-analyte information representing spatial frequency components (e.g.,L>2048, where L<H=k+m+j) present in the conditioned feature whichgenerally represent the frequencies related to scattering events. Thelength of a resulting modified Zyoton vector after a collision istypically greater than L (in the frequency domain) and greater than

(in the time domain, as described with reference to FIGS. 24-27), andmay contain additional frequency components as a result of theconditional bracketed interactions described below. These additionalcomponents may be removed by truncation during renormalization. Eachcollision interaction in one collision iteration, as described below,may correspond to a point on the collision grid and can describe atleast in part the propagation of the two colliding waveforms. In thetime domain or in the frequency domain, the length of the collision gridcan take on values such as 10, 100, 1000, or up to 1,000,000 grid pointsor more.

Thus, the original Zyoton and the collision operator are synthesizedsuch that the first k frequency components of the modified Zyotonresulting from the collision between the original Zyoton and theconditioned feature can represent a feature energy component to bequantitated. For example, referring to FIG. 9, in one instance the firstk frequency components may represent E_(A1), i.e., the energy absorbedby the analyte at the wavelengths associated with Feature F1. In anotherinstance, the first k frequency components may represent, E_(C) ₁ ₁,i.e., the energy absorbed by the confounder C¹ at the wavelengthsassociated with the Feature F1. The first k frequency components mayalso represent the total energy absorbed by two or more, or allconfounders, e.g., E_(C1). In some instances, the first k frequencycomponents of the conditioned feature may represent essentially thetotal energy absorbed by the analyte and by one or more confounders,e.g., (E_(A1)+E_(C1)). In general, with a properly designed Zyoton andcollision operator, the first k frequency components do not representthe lost energy E_(L1).

In a collision computer, in the first iteration, the original Zyoton andthe conditioned feature, each of which represents a traveling waveformin the computer memory, and are synthesized as described below, arecomputationally collided. This collision is “nearly elastic.” In aperfectly elastic collision between a Zyoton and another waveform, thedispersion velocity of the Zyoton after the collision would be the sameas the dispersion velocity of the Zyoton before the collision. Thiswould typically occur only when a Zyoton collides with another solitonwaveform.

In a generally inelastic collision, the post-collision dispersionvelocity of a Zyoton colliding with another waveform would besignificantly different (e.g., greater than 1%, 2%, 5%, 10%, 20%, etc.)than the dispersion velocity of the original Zyoton, and the Zyoton maybe destroyed during the collision. In the nearly elastic collisiondescribed herein, the colliding waveforms, i.e., a Zyoton, and aconditioned feature or a renormalized Zyoton colliding with the Zyoton,are constructed such that during the collision the conditioned featureor the renormalized Zyoton perturb the Zyoton only within specifiedlimits. These limits are generally established by the limits on apermissible change in dispersion velocity, as specified by one or moreKappa parameters and/or by a permissible change in waveform divergence,as specified by the divergence parameter T. In general, the differencebetween the velocity of the original Zyoton and the velocity of themodified Zyoton resulting from the collision is limited to a specifiedthreshold numerical limit, which can be tested using a suitable Kappatest as described above. In various embodiments, to ensure anear-elastic collision, the collision operator is constructed such thatthe divergence of the post-collision waveform, i.e., the modifiedZyoton, is not greater than a pre-set divergence parameter τ, asdescribed in detail below.

As such, in various embodiments, the difference between the pre- and thepost-collision dispersion velocities, i.e., a scaled velocity of theoriginal Zyoton and the velocity of the renormalized Zyoton do notexceed a specified numeric threshold, denoted κ_(DV1). A similarconstraint can also be applied to the difference between the scaleddispersion velocity of the original Zyoton and the velocity of aconditioned feature, where the threshold is designated κ_(DV2). Fornoninvasive glucose measurement, where the spectral energy of the Zyotonwaveform before scaling is about three orders of magnitude higher thanthe spectral energy of the conditioned feature waveform, an example ofthe threshold κ_(DV2) is 1×10⁻⁶.

Velocities of Zyotons and Conditioned Features

The frequency domain amplitudes of the k, m, and j frequency componentsof an original Zyoton are denoted A_(k), A_(m), and A_(j), respectively.The frequency domain amplitudes of the corresponding k, m, and jfrequency components of a co-dependent conditioned feature are denotedas a_(k), a_(m), and a₁, respectively. Once A_(k) are chosen, thecorresponding a_(k) can be determined using a scaling coefficient α. Thescaling coefficient α may be selected such that the two co-dependencyconditions are satisfied. Specifically, the difference between thescaled velocity of the original Zyoton and the velocity of theconditioned feature do not exceed a specified threshold κ_(DV2), and thedivergence of the post-collision modified Zyoton do not exceed aspecified threshold τ. The velocity condition can be tested by scalingthe velocity of the conditioned feature instead of or in addition toscaling the velocity of the original Zyoton. A suitable Kappa thresholdmay be used accordingly.

In various embodiments, if the κ_(DV2) test fails, the frequency domainamplitudes of the frequency components of the conditioned feature areadjusted by applying a scaling coefficient to the correspondingfrequency domain amplitudes of the frequency components of the originalZyoton. Thus:

${{a_{k} = {\frac{1}{\alpha}A_{k}}};{a_{m} = {\frac{1}{\alpha}A_{m}}};{{{and}\mspace{14mu} a_{j}} = {\frac{1}{\alpha}A_{j}}}},$where A_(k), A_(m), and A_(j) are vectors.

The time-domain amplitudes of the Z peaks of the original Zyoton aredenoted as

_(Z) and the time-domain amplitudes of the CF peaks of the conditionedfeature are denoted as

_(CF). The respective velocities of the original Zyotons and theconditioned feature are functions of

_(Z) and

_(CF), respectively, denoted as v(

_(Z)) and v(

_(CF)), respectively. Once a conditioned feature is generated, thevelocity-based co-dependency condition can be tested in the time domainas: |α_(C)*v(

_(Z))−v(

_(CF)|≦κ_(DV2), where α_(C)*v(

_(Z)) is the scaled velocity of the original Zyoton. In the time domain,the velocity of a waveform associated with the collision process (e.g.,a Zyoton, a conditioned feature, a modified Zyoton, and/or arenormalized Zyoton) can be computed as L1 or L2 norm of the amplitudesof a selected number of sideband envelopes, such as those of a Zyotonthat are shown in FIGS. 12A-12C. In the frequency domain, the velocityof a waveform can be represented by L1 or L2 norm of the frequencydomain amplitudes of the first k, i.e., the analyte-informationrepresenting components of the waveform.

As discussed above, α_(C) is the nominal scaling coefficient applied toachieve a desired ratio (α_(Z)) of spectral energy of the Zyoton to thespectral energy of a conditioned feature computed using a fixed number(e.g., 6 in one embodiment) of k frequency components, by adjusting theamplitude of the frequency components of the Zyoton so that the spectralenergy difference between the scaled Zyoton and the conditioned featureis less than κ_(DV2). As noted above, depending on whether the testingand/or scaling is performed in the time domain or in the frequencydomain, a domain-specific value of the applicable Kappa variable is usedin various embodiments.

The term nominal scaling coefficient is used because different featuresfrom the same or different spectra, from the same or different samples,are likely to result in slightly different scaling coefficients tomaintain a fixed relationship, α_(Z), between the spectral energy ofZyoton and spectral energy of the conditioned feature prior to the firstcollision. The following condition is imposed on the nominal ratio:|(α_(C)−α_(Fi) _(_) _(MAX))/α_(C)|≦e.g., 0.1, 0.2, 0.5, or 1.0, and|(α_(C)−α_(Fi) _(_) _(MIN))/α_(C)|≦e.g., 0.1, 0.2, 0.5, or 1.0, whereα_(Fi) _(_) _(MIN), α_(Fi) _(_) _(MAX) respectively denote the maximumand minimum scaling coefficients required to achieve the desired ratioof the spectral energy of the conditioned feature to the spectral energyof the Zyoton, computed using a preset number of frequency components,for all conditioned features to be collided with the same Zyoton. Insome embodiments, |(α_(C)−α_(Fi) _(_) _(MAX))/α_(C)|≦0.1 and|(α_(C)−α_(Fi) _(_) _(MIN))/α_(C)|≦0.1.

EXAMPLES OF WAVEFORM ENERGIES

It is to be understood that in this disclosure, the terms “stronglyabsorbing” and “weakly absorbing” spectral regions (or similar terms,such as “high absorbing” spectral regions and “low absorbing” spectralregions) as used in connection with the measurement of an analyte, referonly generally to absorption within the pure-component spectrum of asubstance which may be either an analyte or a confounder. Thus, for aparticular substance, the spectral regions which are strongly absorbinggenerally have a higher level of absorbance than the spectral regionsthat are weakly absorbing, but those terms do not imply any sort ofstrict mathematical relationship between the absorption values of thetwo regions, nor do they imply any relationship among the absorptionvalues of two different substances. In some cases, a region identifiedas strongly absorbing in one context could be considered weaklyabsorbing in a different context and vice versa. For example, in ageneral broad region of low analyte absorption, some sub-regions mayhave higher absorption than some other sub-regions. Similarly, highanalyte absorption can be significantly low, in absolute terms, relativeto a low confounder absorption.

Similarly, the terms “analyte regions” or “analyte features” and“non-analyte regions” or “non-analyte features” as applied to spectralregions or features, refer only generally to variations in absorbancedue to the analyte. Generally, the absorbance of an analyte in ananalyte feature is greater than in non-analyte features, but in somecases, the absorbance of the analyte in a non-analyte feature orspectral region may be actually higher than the absorbance in an analytefeature or region. This situation can occur because the designations“analyte feature” and “non-analyte feature” may take into considerationthe absorbance of one or more confounders, or even a dominantconfounder. As noted above in describing “strongly absorbing” and“weakly absorbing” spectral regions, the terms “analyte regions” or“analyte features” (e.g., GL features, for glucose measurement, PPGfeatures for PPG measurement, etc.) and “non-analyte regions” or“non-analyte features” (e.g., NO-GL features, NO-PPG features, etc.), asapplied to spectral regions or features, do not imply any sort of strictmathematical relationship between the absorption values of the analytein those regions or features. Rather, they serve to describe the mannerin which the regions or features are used, as further described below.

The table below describes energies at various stages for a feature in aspectral region where the analyte, if present, is known to absorbstrongly, using nominal example values to illustrate the process.

TABLE 3 Example Description Value Symbol Energy of original Zyoton 1000E Energy absorbed by an 1 Δe analyte, as represented by one feature Thegoal is to obtain net energy gain of 1 after 

 collisions Energy of conditioned 10 e; represents Δe, i.e., 1 featureEnergy of modified Zyoton 1000.10

 {E, e} → E₁; E₁ depends on e after the first collision which is theenergy of the conditioned feature.

 represents the collision operation. As the collision is inelastic, E₁ <E + e Energy of the renormalized 0.15 e₁ = 

 (E₁) ≈ (E₁ − E) where modified Zyoton after the e₁ is obtained byremoving, first collision approximately, the energy (E) of the originalZyoton from the modified Zyoton.

 represents an embodiment of the renormalization operation describedherein. As the collision is inelastic E₁ < E + e, e₁ < e Energy ofmodified Zyoton 1000.12

 {E, e₁} → E₂, where C is the after the second collision collisionoperator Energy of the renormalized 0.18 e₂ = 

 (E₂) ≈ (E₂ − E), where modified Zyoton after the

 is the renormalization operator second collision Energy of modifiedZyoton 1000.67

 {E, e_(k−1)} → E_(k) after k collisions Energy of the renormalized 0.81e_(k) = 

 (E_(k)) ≈ (E_(k) − E) modified Zyoton after k collisions . . . . . . .. .

The table below describes energies at various stages for a collisioninvolving a feature in a spectral region where the analyte, if present,is known to absorb weakly. This feature could be from a spectral regionwhere confounders show high absorption, using nominal example values toillustrate the process.

TABLE 4 Description Example Value Symbol Energy of original Zyoton 1000E Energy absorbed by feature 0.001 Δe The goal is to obtain no netenergy gain or a gain of ≦0.001 after 

 collisions Energy of conditioned 10 e; represents Δe, i.e., 1 featureEnergy of modified Zyoton 1000.0004

 {E, e} → E₁; E₁ depends on e after the first collision which is theenergy of the conditioned feature. As the collision is inelastic, E₁ <E + e Energy of the renormalized 0.00006 e₁ = 

 (E₁) ≈ (E₁ − E) where modified Zyoton after the e₁ is obtained byremoving, first collision approximately, the energy (E) of the originalZyoton from the modified Zyoton. As the collision is inelastic E₁ < E +e, e₁ < e Energy of modified Zyoton 1000.0007

 {E, e₁} → E₂ after the second collision Energy of the renormalized0.0009 e₂ = 

 (E₂) ≈ (E₂ − E) modified Zyoton after the second collision Energy ofmodified Zyoton 1000.0009

 {E, e_(k−1)} → E_(k) after k collisions Energy of the renormalized0.002 e_(k) =  

 (E_(k)) ≈ (E_(k) − E) modified Zyoton after k collisions . . . . . . .. . Energy of modified Zyoton 1000.004 or 1000.000081

 {E, e_(N−1)} → E_(N) after 

 collisions (could be greater or less than 0.00001) Energy of therenormalized 0.004 or 0.000032 (could be e_(N)= 

 (E_(N)) ≈ (E_(N)− E) modified Zyoton after 

greater or less than 0.00001) e_(N) ≈ Δe collisions

In the same example, the “net renormalized spectral energy gain,” after

collisions, for a feature pair (with one feature covering the analyteabsorption spectral region and a second feature covering a spectralregion where the analyte is known not to absorb strongly, but withstrongly absorbing confounders), can be computed asΔe=1.060−0.004=1.056. Using calibration tables, this result value, i.e.,1.056, can be used to obtain the concentration of the analyte present inthe sample as used in this example.

Amplitude Notation

In the table and discussion below, upper case letters represent Zyotonamplitudes; lower case letters represent conditioned feature amplitudes.Plain symbols without any prime represent the original Zyoton; symbolswith a single prime represent a modified Zyoton; and symbols with doubleprime represent a renormalized modified Zyoton. Symbols representing thek-th iteration, representing a collision between the original Zyoton andthe renormalized Zyoton generated after the (n−1)-th collision, includesuperscript “(n).” For the sake of convenience, the superscript (1),indicating the modified and renormalized Zyotons generated after thefirst collision, is omitted. Ordinary, non-stylized letters representfrequency domain amplitudes; stylized letters represent time domainamplitudes. Thus:

TABLE 5 Symbol Meaning A_(k), A_(m), and A_(j) Frequency domainamplitudes of the k, m, and j frequency components of the originalZyoton, respectively. In general, k, m, and j are greater than one and,as such, A_(k), A_(m), and A_(j) are row or column vectors of k, m, andj elements, respectively. a_(k), a_(m), and a_(j) Frequency domainamplitudes of the k, m, and j frequency components of the conditionedfeature, respectively A′_(k), A′_(m′), and A′_(j′) Frequency domainamplitudes of the k, m, and j′ frequency components of the modifiedZyoton after the first collision/iteration, respectively. Compared tothe original Zyoton, the modified Zyoton may have different m and jfrequency components, denoted m′ and j′ frequency components A″_(k),A″_(m), and A″_(j) Frequency domain amplitudes of the k, m, and Morespecifically, j frequency components of the renormalized A″_(k) =A_(k)″⁽¹⁾; A″_(m) = Zyoton after the first iteration or collision,A_(m)″⁽¹⁾; and A″_(j) = A_(j)″⁽¹⁾ respectively. Due to renormalization,the renormalized and original Zyotons have the same k, m, and jfrequency components in terms of frequencies, though their respectivefrequency domain amplitudes are different. Typically, A″_(k) is lessthan A_(k) by a factor of 1,000. A_(k)″⁽²⁾; A_(m)″⁽²⁾; and Frequencydomain amplitudes of the k, m, and A_(j)″⁽²⁾ j frequency components ofthe renormalized Zyoton after the second iteration or collision,respectively.

 = [ 

 . . . , 

 ] Time domain amplitudes of l_(Z) peaks of the original Zyotoncontaining l peaks. Dispersion velocity of the original Zyoton isproportional to the time domain amplitude of one or more b sidebandpeaks (as exemplified in FIG. 12C) excluding the strongest peak of theZyoton waveform, denoted 

 . For example b_(Z) = l_(Z) − 1.

 = [ 

 . . . , 

 ] Time domain amplitudes of l_(CF) peaks of the conditioned feature.Dispersion velocity of the conditioned feature is proportional to thetime domain amplitude of one or more b side- band peaks (as exemplifiedin FIG. 12C excluding the strongest peak of the conditioned featurewaveform, denoted 

 . For example, b_(CF) = l_(Z) − 1. In the general case, it is assumedthat prior to a collision, even though the number of space-time pointsin the Zyoton and the condi- tioned feature are the same, the number ofpeaks in the Zyoton (l_(Z)) can be different than the number of peaks inthe conditioned feature (l_(CF)).

Co-Dependency of Waveforms

In various embodiments, the nearly elastic collision described hereinsatisfies two conditions: (i) that the collision must not be perfectlyelastic, and (ii) that the collision must not be generally inelastic.According to the first condition, the collision is not perfectly elasticso that the original Zyoton and the post-collision, modified Zyoton arenot identical. Specifically, with reference to FIG. 11, the collectiveenergy of the first k frequency components of the modified Zyoton,denoted by scalar SE_A′_(k) is greater than the collective energy of thefirst k frequency components of the original Zyoton, denoted by scalarSE_A_(k). The spectral energy SE_A_(k) can be computed as the L1 or L2norm of the amplitude vector A_(k), and the spectral energy SE_A_(k) canbe computed as the L1 or L2 norm of the amplitude vector A′_(k).Similarly, the spectral energy of the conditioned feature, denotedSE_a_(k), can be computed as the L1 or L2 norm of the amplitude vectora_(k).

In general, the dispersion velocity of a waveform (also called thevelocity) is proportional to the spectral energy thereof. Therefore, thevelocity of a Zyoton is proportional to the L1 or L2 norm of thefrequency-domain amplitudes of all k, m, and j components of the Zyoton,represented by the combined amplitude vector [A_(k), A_(m), A_(j)]. Inmany embodiments, the spectral energy of the k components (theanalyte-information representing components) is significantly greaterthan the spectral energy of the m transition components and the jnon-analyte information representing components. As such, in someembodiments, the velocity of a waveform associated with a collision isproportional to the spectral energy of the analyte-informationrepresenting k components of that waveform.

Thus, in some embodiments the velocity of the original Zyoton, denotedv(Z), is represented by SE_A_(k). The velocity of the conditionedfeature, denoted v(CF), is represented by SE_a_(k). Therefore, invarious embodiments, the second requirement of near elasticity, i.e.,the collision must not be inelastic, can be met by synthesizing theZyoton and the carrier kernel and, optionally, by scaling the Zyoton,such that the scaled velocity of the Zyoton is not different from thevelocity of the conditioned feature by κ_(DV2). This test can beexpressed as: |α_(T)*SE_A_(k)−SE_a_(k)|≦κ_(DV2). Instead of scaling thevelocity of the Zyoton, or in addition to such scaling, the velocity ofthe conditioned feature can be scaled during this test.

In the time domain, the dispersion velocity of a waveform isproportional to the L1 or L2 norm of the sideband peaks excluding thehighest peak by amplitude. The velocity can be approximated by aselected number of prominent sideband peaks instead of considering allpeaks. Therefore, in some embodiments the velocity of the originalZyoton, v(Z), is represented by the L1 or L2 norm of the sidebandamplitudes [

₂, . . . ,

_(l) _(Z) ], where the amplitude

₁ of the highest peak of the Zyoton waveform is excluded. There is norequirement for one-to-one or direct correspondence between the first kfrequency components of a Zyoton and the l_(Z) peaks of the time-domainZyoton waveform. Similarly, the velocity of the conditioned feature,v(CF), can be represented by the L1 or L2 norm of the sidebandamplitudes [

₂,

_(l) _(CF) ], where the amplitude

₁ of the highest peak of the conditioned feature waveform is excluded.As such, in some embodiments, the velocity test to ensure the secondrequirement of inelasticity can be expressed as: |α_(T)*∥[

₂, . . . ,

_(l) _(Z) ]∥−∥[

₂, . . . ,

_(l) _(CF) ]∥|≦κ_(DV2). The double bars represent the L1 or L2 norm ofthe amplitudes. The scaling factor α_(T) and the Kappa parameter κ_(DV2)can take on different values based on whether the test is performed inthe frequency domain or in the time domain.

After the first collision iteration, a modified Zyoton is generated. Theco-dependency of the original Zyoton and the modified Zyoton can betested in the frequency domain, to ensure that the collision was nearelastic, by testing the condition: |SE_A_(k)−SE_A′_(k)|≦κ_(DV3). In thetime domain, velocity test can be performed as: |∥[

₂, . . . ,

_(l) _(Z) ]∥−∥[

′₂, . . . ,

′_(l) _(Z′) ]∥|≦κ_(DV3). The Kappa parameter κ_(DV3) can take ondifferent values based on whether the test is performed in the frequencydomain or in the time domain. In addition, the divergence test can beperformed in the time domain by determining the widths of selected bpeak envelopes of the original Zyoton, denoted [δ₁, δ₂, . . . , δ_(b)]and the widths of the corresponding peak envelopes of the modifiedZyoton, denoted [δ′₁, δ′₂, . . . , δ′_(b)]. FIG. 19 depicts δ₁, δ₂, andδ₃ as t1, t2, and t3, and δ′₁, δ′₂, and δ₃′ as t1′, t2′, and t3′. Foreach peak-envelope pair, a difference can be computed. In someembodiments, the divergence condition is satisfied if |δ_(p)−δ′_(p)|≦τ,for each p=1, . . . , b. In some embodiments, an L1 or L2 norm of thedifferences (δ_(p)−δ′_(p)) may then be computed. If the L1 or L2 norm isless than the specified threshold τ, the divergence condition isdetermined to be satisfied.

After the modified Zyoton is renormalized, the co-dependency of theoriginal Zyoton and the renormalized Zyoton can be tested in thefrequency domain, to ensure that the next collision iteration would benear elastic, by testing the condition|α_(T)*SE_A_(k)−SE_A″_(k)|≦κ_(DV3). Instead of scaling the velocity ofthe Zyoton, or in addition to such scaling, the velocity of therenormalized Zyoton can be scaled during this test. In some embodiments,the scaling coefficient α_(T) used to scale the velocity of the originalZyoton, represented in the frequency domain by the spectral energy ofthe analyte-information representing k components of the originalZyoton, may be different than that used when the co-dependency betweenthe original Zyoton and the conditioned feature was tested, to accountfor the difference between the energies of the conditioned feature andthe renormalized Zyoton. In some embodiments, the difference between thevalues of κ_(DV2) and κ_(DV3) can account for this energy difference. Insome embodiments, the values of κ_(DV2) and κ_(DV3) can be the same. Inthe time domain, the velocity test between the original Zyoton and therenormalized Zyoton can be performed as: |α_(T)*∥[

₂, . . . ,

_(l) _(Z) ]∥−∥[

″₂, . . . ,

″_(l) _(Z″) ]∥|≦κ_(DV3). Here again, the scaling factor α_(T) and theKappa parameter κ_(DV3) can take on different values based on whetherthe test is performed in the frequency domain or in the time domain.

After the first collision between the original Zyoton and theconditioned feature, in some embodiments, the subsequent collisionsoccur between a renormalized Zyoton from a preceding iteration(typically the previous iteration), and the original Zyoton or a newZyoton. For the i-th collision iteration, the velocity of the originalZyoton, if used in that iteration, is v(Z). The velocity of the othercolliding waveform is the renormalized Zyoton from the previouscollision iteration, and the velocity thereof is denoted v(Z″_((i−1))).The velocity of the modified Zyoton generated in the i-th iteration isdenoted v(Z′i) and the velocity of the renormalized Zyoton generated inthe i-th iteration is denoted v(Z″i). As described above, thesevelocities can be computed in the frequency domain or in the timedomain.

Optionally, prior to the i-th collision iteration, the velocity test|α_(T)*v(Z)−v(Z″_((i−1))|≦κ_(DV1) is performed. Optionally, after thei-th collision iteration, but before the corresponding renormalization,the velocity test |v(Z)−v(Z′_((i))|≦κ_(DV3) is performed. Optionally,the divergence test using the envelope peaks of the original Zyoton Zand the modified Zyoton Z′_(i) is performed. Optionally, after therenormalization corresponding to the i-th collision iteration, thevelocity test |α_(T)*v(Z)−v(Z″_(i))|≦κ_(DV1) is performed. One or moretests may be performed in each collision iteration and in differentcollision iterations, different tests may be performed. The collectiveobjective of these tests, however, is that each collision iteration isnear elastic as described above, and that the colliding waveforms areco-dependent.

To illustrate a collision of the two traveling waveforms in thefrequency domain, the k, m, and j frequency components of both theZyoton and the conditioned feature are depicted (as shown in FIG. 11) asordered from left to right. A Zyoton or a conditioned feature can berepresented as frequency components increasing from left to right orcould be represented as frequency components increasing from right toleft. The ordering of the frequency components is based on the powerspectral densities (PSDs) of the respective frequency components. Insome embodiments, the PSD of the k components>the PSD of the mcomponents>the PSD of the j components. In some embodiments, the PSD ofthe k components<the PSD of the m components<the PSD of the jcomponents.

The conditioned feature and the original Zyoton are synthesized suchthat the increase in the collective energy of the first k frequencycomponents of the original Zyoton due to a collision is proportional tothe collective energy represented by the first k frequency components ofthe conditioned feature. As described above, the first k frequencycomponents of the conditioned feature may capture E_(A1), E_(C1),(E_(A1)+E_(C1)), a fraction of E_(C1), e.g., E_(C[n])=Σ_(i=1) ^(n) E_(C)_(i) ₁, where there are a total of N confounders and n<N, or(E_(A1)+E_(C[n])). As such, after the first collision,(∥A′_(k)∥−∥A_(k)∥) can be proportional to any one of E_(A1), E_(C1),(E_(A1)+E_(C1)), E_(C[n]), and (E_(A1)+E_(C[n])). These feature energyquantities, generally referred to as E_(M1), represent the concentrationof a material (e.g., the analyte, a combination of the analyte and atleast some confounders, a single confounder, or a combination of atleast some confounders) in the medium. Therefore, a change in thespectral energy of a post-collision result (e.g., a Zyoton perturbed bya conditioned feature) relative to the spectral energy of the originalZyoton can be used to estimate the concentration of material exhibitedin the spatial, temporal or spectral window defined by the feature.

According to the second condition, the collision is not generallyinelastic, i.e., at a minimum, the collision operation does notintroduce into the modified Zyoton any new frequency components withinthe first k frequency components that were not present in the originalZyoton. Introduction of such frequency components can represent energiesthat are not related to the energies absorbed by the analyte and anyconfounders. Therefore, if any such frequency components are introduced,the difference (∥A′_(k)∥−∥A_(k)∥) may not accurately represent theconcentration of material exhibited in the spatial, temporal, orspectral window defined by the feature. A Zyoton design rule requiresthat the conditioned feature and the Zyoton not introduce new frequencycomponents in the set of the first k Zyoton frequency components. Insome embodiments, this is ensured by scaling the Zyoton waveform energyto be approximately three or more orders of magnitude higher than thespectral energy of the conditioned feature with which it is collided.

In an embodiment for glucose measurement, where: (i) the absorbancelevel due to the analyte may be less than 0.01% of the total absorbance,and (ii) there can be up to a three orders of magnitude dynamic range ofthe analyte (i.e., glucose) concentration range, in the first collision,the threshold value κ_(DV2) used to ensure that the Zyoton energy is atleast three orders of magnitude greater than the energy of theconditioned feature can be 1×10⁻⁶. Recall, the Kappa threshold is alsoused in the velocity test described above, to ensure the co-dependencyof the Zyoton and the conditioned feature to be collided therewith. Ingeneral, the threshold κ can be decreased as the collision iterationcount is increased. Thus, as the number of collision iterationsincreases, the amount of dispersion permitted in each iteration canbecome smaller.

While the difference (∥A′_(k)∥−∥A_(k)∥) after the first collision canrepresent E_(M1) (i.e., any one of E_(A1), E_(C1), (E_(A1)+E_(C1)),E_(C[n]), and (E_(A1)+E_(C[n]))), the accuracy of such representationcan be improved, especially when the signal-to-clutter ratio (SCR) islow, using several collision iterations. In various embodiments, theelasticity of a single collision, as measured by κ_(DV1), whichcorresponds to a collision between the original Zyoton and arenormalized Zyoton, is generally inversely proportional to the SCR. LowSCR generally implies that the value of κ_(DV1) for insuring compliancewith co-dependency condition is small, e.g., a value of 1×10⁻⁶ used fora SCR of 10⁻³ or a value of 1×10⁻⁸ for a SCR of 10⁻⁴ and, as such, thechange in the velocity of the modified Zyoton, and the correspondingrenormalized Zyoton, relative to the velocity of the original Zyoton issmall. For an order of magnitude reduction in SCR, the threshold κ_(DV1)may be generally reduced by two orders of magnitude. As the permittedchange in the dispersion velocity after one collision is small, theobserved change in energy after one collision, i.e., (∥A′_(k)∥−∥A_(k)∥),is also small. Therefore a single collision iteration may not besufficient to produce a discernible change in the spectral energy due toanalyte absorption estimated using the first k frequency components. Theenergy change after a single collision may be only visible if k werelarge or if the window length approaches the total number of frequencycomponents of the conditioned feature. The latter case, however, canrepresent change in energy due to not only analyte and/or confounderabsorption, but also due to energy loss or absorption of energy in themedium. Therefore, several collision iterations may be required toinduce a change in the spectral energy computed using the first kfrequency components to discern and characterize changes due toabsorption by the analyte and/or one or more confounders.

In one embodiment, the subsequent collisions involve the modified Zyotonand the original Zyoton. Therefore, before the next collision, themodified Zyoton is renormalized to remove therefrom the spectral energyof the original Zyoton so that the gain in the energy of the originalZyoton caused in the next iteration is proportional substantially onlyto E_(M1), as represented by the modified Zyoton produced in thesubsequent iteration. As used herein, substantially means thecontribution from noise and/or clutter is no more than 0.01%, 0.2%,0.5%, 1%, 10%, etc. As explained above, in applications with extremelylow SCR (e.g., SCR<10⁻⁴) the (∥A′_(k)∥−∥A_(k)∥) may be nearly zero postrenormalization. This can lead to numerical instabilities in thecomputation, such as divide-by-zero instabilities. To prevent suchinstabilities, book-keeping is employed, e.g., by ensuring that aftereach collision, or at least after a selected number of successiveiterations (e.g., 2, 3, 5, 10, 25, 50, etc.), the total change betweenthe energies of the first k frequency components of the modified Zyotonand the energy of the first k frequency components of the originalZyoton monotonically increases. This change may be tracked as a changein the ratio of energies of the k frequency components of the modifiedZyoton and original Zyoton from a starting value of unity (i.e., 1) or100%.

In addition, post-collision renormalization can compensate for theimpact of any pre-collision up-scaling of any entity participating in acollision (e.g., the Zyoton, the conditioned feature, and/or therenormalized Zyoton from the previous iteration) or the down-scaling ofany of these entities by the factor α, as described below. For example,the down-scaling of the modified Zyoton waveform, to obtain arenormalized Zyoton, removes some of the inherent waveform energy.

As described above, this renormalization computation typically targetstwo objectives in the same computational step. Specifically, in thefirst objective of renormalization, it is necessary to remove thespectral energy of the original Zyoton. In addition, it is oftennecessary to compensate for the energy of frequency components that wereremoved in any post-collision down-sampling step, also calledtruncation. Without this compensation, numerical artifacts and energyinaccuracies may be introduced into follow-on collision iterations. Thefirst aspect of the renormalization is generally directed to the removalof the energy of the k components of original Zyoton from the modifiedZyoton, often producing a renormalized Zyoton in which the amplitudes ofthe first k frequency components are similar to the respectiveamplitudes of the first k frequency components of the conditionedfeature.

The second aspect is generally directed to preserving the energycontributions of any frequency components in the modified Zyoton thatwere removed post-collision for computational efficiency, and/or toensure that the subsequent collision iterations would be near-elastic,as described above. In particular, any new frequency components that aretransition (i.e., m) components and/or non-analyte-informationrepresenting (i.e., j) components, can cause a subsequent iteration tobe inelastic. As such, one or more of these new frequency components areremoved, but the energy thereof is redistributed among the surviving mand/or j components. Alternatively or in addition, one or moretransition components and/or one or more non-analyte-informationrepresenting components that were present in the original Zyoton and/orthe conditioned feature may be removed, and the energy thereof may beredistributed among the surviving m and/or j components.

Therefore, referring again to FIG. 11, the amplitudes of all of the k,m, and j components of the modified Zyoton, denoted [A′]=A′[1, . . . ,k+m+j], are scaled using a renormalized scaling vector α, computed basedon the amplitudes of the k components of the original Zyoton and thecorresponding k components of the modified Zyoton. In some embodiments,the scaling vector α is based on a ratio S₁ of the spectral energy ofthe k components of the original Zyoton and the spectral energy of thecorresponding k components of the modified Zyoton, expressed as:

$S_{1} = {\frac{A_{k}}{A_{k}^{\prime}}.}$In some embodiments, this can cause the respective amplitudes of variousor all components of the renormalized modified Zyoton, denoted[A″]=A″[1, . . . , k+m′+j′] to be within 10%, 20%, or 50%, etc.,respectively, of the amplitudes of the corresponding frequencycomponents of the conditioned feature, denoted [a]=a[1, . . . , k+m+j].Thus:[A″]=S ₁ [A′]

A[1, . . . ,k+m′+j′]≈a[1, . . . ,k+m+j]  (9)In some embodiments, the a preset amount of energy, e.g., E* is removed.To this end, a pre-set scaling vector S₁=[S₁ ¹, S₁ ², . . . , S₁ ^(k), .. . , S₁ ^(k+m+j)] may be used to scale the amplitudes of the componentsof the modified Zyoton [A′]. The energy level E* can be selectedaccording to the energy of the original Zyoton or independently thereof.

The cardinality of the transition components of the modified Zyoton,denoted m′, and the cardinality of the non-analyte-informationrepresenting components of the modified Zyoton, denoted j′, indicatethat the modified Zyoton may have some new transition and/ornon-analyte-information representing components. Any of these transitionand/or non-analyte-information representing components, including newand/or previously existing ones, may be removed during truncation. Theamplitudes of some or all of the surviving transition and/ornon-analyte-information representing components of the modified Zyotonmay then be adjusted further using another scaling factor S₂, such thatthe spectral energy of the surviving m and j components of therenormalized Zyoton is approximately equal to the spectral energy of allof the transition and/or non-analyte-information representing componentsof the modified Zyoton after scaling thereof but its truncation. Thus:[A″ _(m,j) ]=S ₂ [A′ _(m,j)]_(TR)   (10)where [A′_(m,j)]_(TR) represents a modified Zyoton as truncated. Thescaling factor S₂ may be based on the ratio

$\frac{S_{1} \times {A_{m^{\prime},j^{\prime}}^{\prime}}}{A_{m,j}}.$

A subsequent collision between the original Zyoton and the renormalizedmodified Zyoton yields a second modified Zyoton. The spectral energy ofthe first k frequency components of the second modified Zyoton isdenoted ∥A′⁽²⁾ _(k)∥, and the difference (∥A′⁽²⁾ _(k)∥−∥A_(k)∥) canrepresent E_(M1) ⁽²⁾, which is a refined estimate of E_(M1), i.e., arefined estimate of any one of E_(A1), E_(C1), (E_(A1)+E_(C1)),E_(C[n]), and (E_(A1)+E_(C[n])). After a selected number of iterations,

which can vary from one embodiment to another, as described below,

can provide an accurate estimate of the energy absorbed at thewavelengths associated with the feature F1 by the concentration of amaterial in the medium to be analyzed. As described above, in thegeneral case, the material can be only the analyte, a single confounder,a combination of one or more confounders, or a combination of theanalyte and one or more confounders.

The above described process can be repeated for another feature F2 toobtain

. In some embodiments, the two features F1 and F2 are selected such thatthere is a difference between the absorption of at least one constituentof the material (i.e., the analyte and/or at least one confounder) inthe respective wavelengths bands of the two features. Therefore, thedifference between

and

or a function of these two variables can be used in determining theconcentration of the constituent that absorbs differently in the twowavelength bands. In one embodiment for noninvasive glucose measurement,in which the analyte does not absorb substantially in the wavelengthbands of the Feature F2 and if the total absorption of the confoundersremains substantially unchanged between the wavelength bands of FeaturesF1 and F2, and where

represents (E_(A1)+E_(C1)) and

represents E_(C2), the difference (

−

) can represent E_(A1), which can be used in determining theconcentration of the analyte. These specific conditions generally maynot be true, however. Therefore, particular functions or relations, asdescribed below, based on the estimates of energies corresponding to oneor more features and/or one or more feature pairs can be used todetermine more accurately the concentration of the analyte.

Synthesis of Zyotons and Carrier Kernels

With reference to FIG. 10B, a feature is generally related to theintensity of radiation reflected from or transmitted through a medium,or to the absorption of incident radiation within the medium to beanalyzed, corresponding to a specified range of wavelengths [λ1, λ2],also called feature boundaries. Typically, a feature (e.g., Feature F1)does not have a smooth profile as shown in FIG. 10B. Examples ofintensity and absorbance spectra are shown in FIGS. 31A and 31B. Thefeatures obtained from any of these spectra, typically have asaw-toothed, somewhat jagged profile, such as that shown in FIG. 32.Such a profile generally results from sampling errors, device anddetector noise, ADC discretization artifacts, and/or path length effectsof summing absorbance from many individual NIR photons. Noise in anintensity spectrum produced from radiation collected at a detectortypically results from several sources. The quantization error of theanalog-to-digital converter (ADC) is one source. Another source of noiseis the variation in total travel distances of individual photons as theypropagate through a medium to be analyzed (e.g., the skin tissue), andthis variation in combination with scattering losses within the mediumcan introduce measurement noise in a received or detected intensityspectrum.

Moreover, the noise in an intensity or absorbance spectrum may not beuniform across the spectrum, and may vary according to the wavelength.As such, the noise in a feature within the wavelength range [λ1, λ2] canbe non-uniform and may vary non-monotonically with the wavelength. Thevariations in noise across a spectrum can be determined by thedifference between any single spectrum and a mean spectrum obtained frommultiple spectra generated using the same incident radiation and medium.FIG. 31A provides an example of a diffuse reflectance intensity and FIG.31B shows the associated absorbance from a NIR spectrum from human skin.An example of noise in a captured spectrum is shown in FIGS. 33 through35.

FIG. 33 provides an example of a set of mean-centered absorbance spectrato show instrument related spectral variability as a function of NIRwavelength. FIG. 34 shows an example of wavelength-by-wavelength RMSnoise, based upon a set of spectra. FIG. 35 depicts a difference betweena single spectrum and the mean spectrum and provides an illustration ofthe variation in noise across wavelengths. FIG. 36 shows the scaledintensity and absorbance spectra associated with a single feature on thesame plot. As shown in the legend for FIG. 36, different absorbance andintensities profiles have been normalized by multiplying with differentfactors. The ultra-weak absorbance of pure-component spectrum ofglucose, in the feature region delineated by 1540 nm to 1554 nm, hasbeen multiplied by a factor of 40,000 to plot at the same scale as theabsorbance from confounders: fat (multiplied by factor of 8) and water(multiplied by factor of 2). These scaled absorbances for glucose andthe confounders fat and water are overlaid on the same plot. The legendprovides all the factors used for normalizing the spectra (in intensityor absorbance units) to plot them on the same graph.

The fluctuations in the feature absorbance profiles shown in FIG. 36typically result from sampling errors, device and detector noise,analog-to-digital conversion (ADC) discretization artifacts, and pathlength effects of summing absorbance from the travel-path of manyindividual NIR photons launched in each illumination of the sample. Afeature such as that shown in FIG. 36, thus may have both periodicityand frequency content.

The process of generating a conditioned feature begins with thesynthesis of a Zyoton waveform and a carrier kernel waveform. The Zyotonis generated using a number of frequency components. The first k (e.g.,six) frequency components are selected, e.g., for measuring the energyabsorbed by an analyte (such as energy absorbed by glucose in tissue),according to pure component spectrum of the analyte and thecharacteristics of instrument noise, such as the RMS value in theamplitude domain, power spectral density in frequency domain, and/orperiodicity.

In various embodiments, the selected frequency components are related tofrequencies of radiation that are absorbed strongly by the analyte andthose absorbed weakly or negligibly by the analyte. The analyte-specificfrequency components may be selected following a Fourier transform ofthe selected spectral feature either before or after an optionalinterpolation, a sort of the frequency components by peak power, and aselection of the first k (e.g., 6) frequency components. A Fouriertransform of a feature includes sinusoidal waveforms at differentfrequencies/frequency components that, when summed, represent thefeature waveform.

The feature data extracted from the spectrum has low spatial frequencycontent, often due to a limited data vector length. The spatialfrequency content may therefore be insufficient to characterize changesin the feature properties due to analyte concentration and interferencefrom confounders. Coupling the feature with a complex carrier kernelwith a higher spatial frequency content can provide additional degreesof freedom to characterize the underlying analyte. Pre-cursor modulation10 in FIG. 37 of the feature can also increase the degrees of freedom byincreasing the bandwidth of the feature waveform prior to modulating thecarrier kernel. Different features, associated with different wavelengthregions, with different underlying analyte concentrations generallymodulate the carrier kernel differently.

A carrier kernel typically includes k high amplitude frequencycomponents, where k≧1, and j low amplitude frequency components, wherej>1, and may include m medium-amplitude components. While the specificvalues of the amplitudes of these frequency components can be selectedaccording to the amplitudes of the frequency components of the Zyoton tobe used in the collision process and/or other parameters of thecollision process, the amplitudes of the k high amplitude (also calledhigh energy) frequency components of the carrier kernel are typicallytwo or three orders of magnitude greater than the amplitudes of the jfrequency components of the carrier kernel. The high energy k frequencycomponents are employed primarily for extraction of the energy absorbedby the analyte from a feature.

The carrier kernel may optionally include m frequency components (calledmedium energy components or transition zone components) havingamplitudes that are generally two to three times the amplitudes of thelow energy j components. The Zyoton used during the collision processalso has high energy k components, low energy j components and,optionally, medium energy m components. Likewise, a conditioned featuregenerated by modulating the carrier kernel by a feature also has thehigh energy k components, low energy j components and, optionally,medium energy m components. During various frequency-domainimplementations of the collision process, the respective Zyoton andconditioned feature components are amplitude sorted. Therefore, thediscussion below usually refers to the high-energy components of awaveform (e.g., a Zyoton, a carrier kernel, a conditioned feature, amodified Zyoton, a renormalized Zyoton, etc.), as the first k frequencycomponents or the first k components.

In various embodiments, the first k frequency components of a Zyoton aredetermined by examination of the second derivative of the pure componentspectrum (e.g., glucose) in order to identify areas of the greatest rateof change of energy absorption within the features derived from thespectrum. For example, FIG. 28A depicts an absorbance spectrum ofglucose, and FIG. 30A shows the second derivative of that absorbancespectrum. The ratio of the magnitude of the second derivative in theregions that correspond to high and low analyte absorption regions (asshown in FIG. 28A) may be used to establish the relation (e.g., relativeratio of magnitudes of first k frequency components of the Zyoton and/orthe carrier kernel) between the first k frequency components, asdescribed below with reference to FIG. 38.

The second derivative may also be used, as discussed below, as anindicator of how confounder interference will distort high and lowabsorbing regions in the frequency domain for the specific wavelengthregion from which features are selected. In the absence of noise, thesecond derivative can be used to provide a numerical classifier foridentifying the areas of greatest change in either of the high and lowabsorbance wavelength regions of the pure component spectrum of theanalyte. Use of the second-order derivative is generally described inFerraty, F. and Vieu, P, “The Functional Nonparameteric Model andApplication to Spectrometric data”, Computational Statistics, 17(4),2002, which shows that by taking the second- and higher-orderderivatives, one can focus on curvature rather actual values taken byfunctions to build more robust classifiers and improve predictionperformance in the presence of noise and other uncertainties.

The number k, i.e., the cardinality of the set of high-energycomponents, can be determined by estimating the number of frequencycomponents required to separate (as defined below) spectral regions ofthe second derivative corresponding to higher and lower absorbingregions of the pure component spectrum in the presence of at least threeorders of magnitude of added RMS pseudo-random noise (PRN). Commonlyknown techniques for generating pseudo-random noise may be employed andaddition is typically represented as wavelength-by-wavelength additionof the PRN value to the pure component absorbance amplitude value. Invarious embodiments discriminant classification is further used todevelop a quadratic discriminant classifier using combinations ofdifferent numbers of frequency components, i.e., using 2, 3, 4, . . . kcomponents.

A quadratic classifier can be used to separate two or more classes ofobjects or events by a quadric surface (where quadric is anyD-dimensional hypersurface in (D+1)-dimensional space defined as thelocus of zeros of a quadratic polynomial). In coordinates x₁, x₂, . . ., x_(D+1), the general quadric is defined by the algebraic equation:

$\begin{matrix}{{{\sum\limits_{i,{j = 1}}^{D + 1}{x_{i}Q_{ij}x_{j}}} + {\sum\limits_{i = 1}^{D + 1}{P_{i}x_{i}}} + R} = 0} & (11)\end{matrix}$where x=(x₁, x₂, . . . , x_(D+1)) is a row vector, x^(T) is thetranspose of x (a column vector), Q is a (D+1)×(D+1) matrix and P is a(D+1)-dimensional row vector and R a scalar constant. The values Q, Pand R are often taken to be over real numbers or complex numbers. Theset of “vectors of observations” used in the discriminant analysisincludes features drawn from the selected regions of the secondderivative waveform combined with noise (PRN), each of which isassociated with a higher or lower absorption region of the analyte purecomponent spectrum.

To generate the vectors of observation to be used in discriminantanalysis: (i) the values of the second derivative of the pure componentabsorbance spectrum, to which PRN has been added, in the high and lowabsorbance regions as defined above, are extracted and copied into twonew vectors HighAbs and LowAbs respectively; (ii) in some embodiments,the HighAbs and LowAbs vectors from the pure component absorbancespectrum for the analyte are then both up-sampled to the twice theup-sampled length used for up-sampling a spectral feature vector (e.g.,2*2048=4096) as used in collision computing. The resulting vectors aredenoted as up-sampled-HighAbs and up-sampled-LowAbs vectorsrespectively; (iii) up-sampled HighAbs and up-sampled LowAbs vectors arethen Fourier transformed into spatial frequencies. The results aredenoted as F{Up-sampled HighAbs)} and F{Upsampled LowAbs}vectors.

Additional steps include: (iv) magnitude sort F{Upsampled HighAbs} andF{Upsampled LowAbs} on the basis of the amplitude of frequencycomponents to yield F′{Upsampled HighAbs} and F′{Upsampled LowAbs}vectors; (v) construct observation test vectors, to be used indiscriminant analysis test, by selecting subsets of F′{UpsampledHighAbs} and F′{Upsampled LowAbs} vectors with variable number offrequency components such as v=2, 3, 4, . . . k components, where eachvalue v is a candidate k value; and (vi) optionally repeat this sequenceof step (i)-step (v) 2, 5, 10, 50, 100, or 500 times, where differentamounts of random noise are added to the pure component spectrum togenerate different test sets of observation vectors of different numbersof frequency components.

The value of “k” may then be set to the number of components that canseparate the high and low absorbance noisy second derivative regions ofthe analyte pure component spectra, in the case of a single test, or themaximum number of components that are required to separate these highand low absorbing regions in repeated tests. In various embodiments, thequadratic discriminant technique is used to build a classifier that canassociate combinations of frequency components with the absorptionregions associated with an analyte of interest. In general, high and lowabsorbing spectral regions are said to be separated when the result ofthe discriminant classifier, normalized to a value of 1, is less than0.1, 0.2, or 0.5.

In one embodiment, the number of high energy components (k) of theoriginal Zyoton (and of the carrier kernel, as well), where the k highenergy components represent absorption by the analyte, is determinedusing: (a) the Fourier transform of a noisy signal obtained by adding acertain amount of noise to the second derivative of the analyte purecomponent spectrum, and (b) discrimination classification. Withreference to FIG. 39, the pure component spectrum of the analyte ofinterest, denoted XA, is obtained in step 2. This spectrum is typicallygenerated using the source of radiation and the detector (e.g., anoptical probe, examples of which are described below) to be used in thenon-invasive measurement system. The spectrum XA may be optionallyinterpolated in step 2. In step 4, a second derivative of the spectrumXA, denoted XA″ is obtained.

Pseudorandom noise N^(A) is added to the second derivative XA″, in step6, to obtain a noisy signal S^(A). The noise N^(A) can be gray noisewith a correlation time of 10⁻⁶ seconds, and may have aroot-mean-squared (rms) value that is a multiple of (e.g., 100, 1000,1500, 5000, 10,000 times, etc.), the rms value of the noise introducedby the sensor, i.e., the noise of the spectrum signal XA. Alternatively,the rms value of NA can be a multiple of the RMS value of the first orhigher-order derivative of XA. In step 8, Fourier transform of the noisysecond derivative signal S^(A) is computed to identify the variousfrequency components therein. These components are sorted by amplitudein step 10, though in some embodiments, this step is optional.

Discriminant classification is performed in step 12 to determine thevalue of k, i.e., the cardinality of the set of high-energy componentsof the Zyoton and the carrier kernel. Specifically, k is set to be equalto the number of frequency components of the noisy signal that areneeded to separate the high and low absorbance regions as defined above.Thus, the determination of k for the Zyoton (and for the carrier kernel,as well) is based, at least in part, on the SNR of the measurementsystem. In some embodiments, the value of k may be incremented by asuitable integer constant, e.g., 1, 2, 4, etc. The actual frequencies ofthe k Zyoton and the carrier kernel frequencies are generally determinedby the selected Zyoton family/generator and need not be related to thefrequencies of the components of the noisy second derivative signal. Insummary, k is concluded when the discriminant classification techniqueusing k-components can separate regions of the second derivative of thepure component spectrum corresponding to higher and lower absorbanceregions of the pure component spectrum in the presence of noise.

The next m (e.g., 4, 6, etc.,) frequency components are designed as atransition zone to the lower amplitude j frequency components. Thediscriminant classification technique may be used to determine m, i.e.,the number of frequency components in the transition zone of the Zyoton(and the carrier kernel, as well). With reference to FIG. 40, purecomponent spectra from one or more confounding materials, e.g., urea andcollagen if glucose is the analyte of interest, are added in step 4 tothe pure component spectrum of the analyte (XA) obtained in step 2, toproduce a composite spectrum, denoted XC, in step 4. The secondderivative of the composite spectrum XC, denoted XC″, is obtained instep 6.

In step 8, XC″ is further combined with random white noise N^(C) (e.g.,colored grey noise with correlation time of 10⁻⁶ seconds) having an rmsvalue equal to a multiple (e.g., 100, 1000, 2500, 10,000 times, etc.),the rms value of the signal-to-noise ratio of the second derivative ofthe composite spectrum, i.e., XC″, where all the absorbances of theconfounders are normalized to the maximum absorbance of the analyte. Insome embodiments, the rms value of N^(C) is a multiple of the rms valueof XC, a first derivative thereof, or third and higher-order derivativesof XC. In some embodiments, the rms value of N^(C) is a multiple of therms value of sensor noise, i.e., the rms value of the pure componentspectrum of the analyte XA, or a first or higher-order derivative of XA.The number m of the frequency components required to separate, accordingto the discriminant classification described above, the spectral regionsof the second derivative of the composite spectrum, with added noise,where the separated spectral regions correspond to higher and lowerabsorbance regions of the pure component spectrum of the analyte can bedetermined in steps 10-14. The discriminant classification in step 14may include several trials of different candidate values of m. Thisprovides the number of frequency components k+m. The discriminantanalysis used to determine the number m of the medium energy componentsis similar to the discriminant analysis described above that isperformed in the determination of the number k of the high-energycomponents. In finding m, however, the candidate values for the lengthof the observation vectors for discriminant analysis are set to be oflength k+1, k+2, k+3, . . . , k+m frequency components.

For the determination of j, a dominant confounder may be used in theanalysis. For example, if glucose is the analyte of interest, thespectrum of water (generally known to have much higher absorbance thanglucose in tissue) can be used to create additional distortion. Withreference to FIG. 41, the pure component spectrum of the analyte (i.e.,XA), one or more confounders, and the water spectrum (all normalized tothe absorbance of water, because the water spectrum dominates thespectrum of glucose) are combined to obtain a composite spectrum orsignal, denoted XC⁺ in steps 2 and 4. In step 10, the second derivativeof this composite spectrum, denoted XC⁺″ is mixed with random noise N⁺having, e.g., the A-weighting and correlation time of 10⁻⁶ seconds. Thenoise N⁺ is constructed such that the rms value of N⁺ is a multiple of(e.g., 400, 800, 1000, 2000, 7500, 12,000, times, etc.), the rms valueof the SNR of the second derivative of the composite spectrum XC⁺″.

In some embodiments, the rms value of N⁺ is a multiple of the rms valueof XC⁺, a first derivative thereof, or third and higher-orderderivatives of XC⁺. In some embodiments, the rms value of N⁺ is amultiple of the rms value of XC used to determine m, or the rms value ofthe pure component spectrum of the analyte XA, or a first orhigher-order derivative of XC or XA. Fourier analysis followed bydiscriminant classification are applied in steps 10-14, as in thedetermination of the values of k and m, to determine the number j of thelow-energy components required to separate the spectral regions of thesecond derivative with added noise corresponding to regions of higherand lower absorbance of the analyte pure component spectrum, asdescribed above. Including the water spectrum generally increases therange of the frequency components beyond those corresponding to therandom noise from scattering. Because of the magnitude of the absorbanceof the dominant confounder (water), very small local variations in inits concentration typically manifest as noise in the absorbance that areadded to the noise contribution from light scattered by the medium.

In some embodiments, instead of adding a dominant confounder, randomwhite noise denoted N⁺⁺ (e.g., grey colored random noise with, e.g.,A-weighting and correlation time of 10⁻⁶ seconds) with a magnitude thatis a multiple (e.g., 20, 50, 100, 125, times etc.) the noise N⁺ that wasadded in step 8 is added in step 16 and, optionally, pure componentspectra of one or more confounders are also added to the pure componentspectrum of the analyte XA. Thus, the rms value of the noise N⁺⁺ can be100,000 times the rms value of the SNR of the second derivative of theanalyte pure component spectrum without confounders, i.e., the signalXA″. In some embodiments, the rms value of N⁺⁺ is a multiple of the rmsvalue of XA, a first derivative thereof, or third and higher-orderderivatives of XA. In some embodiments, the rms value of N⁺⁺ is amultiple of the rms value of XC⁺, or XC used to determine m, or a firstor higher-order derivative of XC⁺ or XC. Instead of adding a dominantconfounder spectrum, such as water spectrum, such noise may be added toincrease the frequency range to include the scatter-related frequencycomponents.

The discriminant analysis used to determine the number j of the lowenergy components is similar to the discriminant analysis describedabove that is performed in the determination of the number k of thehigh-energy components and the number m of the medium energy components.In finding j, however, the candidate values for the length of theobservation vectors used for the discriminant analysis are set to be oflength k+m+1, k+m+2, . . . , k+m+j frequency components.

After the values of the number of Zyoton and carrier kernel componentsin the high, medium, and low energy regions, i.e., k, m, and j,respectively, are determined, the actual components of the waveforms areselected. With reference to FIG. 38, the bandwidth and/or amorphological profile of the noisy signal S⁺ (generated in step 8 ofFIG. 41) is computed in step 2 (of FIG. 38). A Zyoton waveform familyand/or a generator is selected in step 2 according to the morphologicalproperties of: (a) the pure component spectrum of the analyte,optionally combined with the pure component spectrum/spectra of one ormore confounders, or (b) the first or higher-order derivative of thepure component or combined spectrum, optionally with added noise. Thefollowing examples illustrate the selection of a waveform family and/orgenerator.

If the spectral bandwidth of the signal used in step 2 is high, e.g.,greater than 1 kHz, 100 kHz, 1 MHz, 100 MHz, etc., high spectralbandwidth Zyotons can be synthesized using waveform families such assolitons; vortex-solitons; wavelets; or multi-color soliton and/or,optionally, using waveform generator functions such as harmonicoscillators or chaotic attractors.

If the spectral envelope of the signal used in step 2 is symmetrical,Zyotons with symmetrical spectral envelop can be synthesized usingwaveform families such as solitons; wavelets; ridgelets; or multi-colorsolitons and/or, optionally, using generator functions such ascyclostationary series or Lyapunov functions. On the other hand, if thespectral envelope of the signal used in step 2 is monotonic, Zyotonswith a monotonic spectral envelop can be synthesized using waveformfamilies such as solitons; autosolitons; similaritons; wavelets;curvelets; ridgelets; bions; or elliptic waves and/or optionally, usinggenerator functions such as Frobenius manifolds; harmonic oscillators;Hermite polynomials; polynomial sequences; asymptotic Hankel functions;or Neumann spherical functions. If the spectral envelope of the signalused in step 2 is random, Zyotons with a random spectral envelop can besynthesized using waveform families such as solitons; multi-colorsolitons; Ricci solitons; or nonautonomous similinear wave equationsand/or, optionally, using generator functions such as random numbergenerators.

If the peak spectral energy of the signal used in step 2 is greater thana selected threshold, Zyotons with high peak energy can be synthesizedusing waveform families such as solitons; autosolitons; self-compressingsimilaritons; vortex-solitons; multi-color solitons; and/or, optionally,using waveform generators such as Gamma functions; Riemann Zetafunctions; polynomial sequences; spatial random fields; sphericalharmonics; chaotic attractors; exponential attractors; or evolutionequation of exponential attractors.

If the spectrum of the signal used in step 2 has linearly distributedamplitudes, Zyotons with a linear amplitude distribution can besynthesized using waveform families such as solitons; autosolitons;similaritons; wavelets; curvelets; ridgelets; and/or, optionally, usingwaveform generators such as Gamma functions; Riemann Zeta functions;polynomial sequences; or spherical harmonics. If the spectrum of thesignal used in step 2 has non-linearly distributed amplitudes, however,e.g., exponentially distributed amplitudes, Zyotons with an exponentialamplitude distribution can be synthesized using waveform families suchsolitons; vortex-solitons; multi-color solitons; and/or, optionally,using waveform generators such as Fractals; poweroid coupled withsinusoidal functions; chaotic attractors; exponential attractors;evolution equation for polynomial nonlinear reaction-diffusion equation;evolution equation for Kuramoto-Savashinsky equation; or evolutionequation of exponential attractors.

In step 4, “k” high energy components are obtained from the selectedZyoton family/generator. This process is repeated in steps 6, 8,respectively, to obtain the m transition components and the j low energycomponents. Each component (e.g., the i-th component) can be representedin terms of its frequency Ω(i) and frequency-domain amplitude A(i).

In some embodiments, a base Zyoton obtained from a Zyotonfamily/generator may be represented in the time domain, as describedabove, as:Z _(N)(xt)=2∂_(x) TrB _(x)(1+B)⁻¹  (12)By applying the Fourier transform to this time-domain representation,the frequency components thereof can be determined. These frequencycomponents of the base Zyoton, each represented as anamplitude-frequency pair <A*_(i), Ω*_(i)>, sorted by the amplitude, canbe expressed in terms of k, m, and j as shown in Table 6:

TABLE 6 Amplitudes A*₁ A*₂ . . . A*_(k) A*_(k+1) . . . A*_(k+m)A*_(k+m+1) . . . A*_(k+m+j) Frequencies Ω*₁ Ω*₂ . . . Ω*_(k) Ω*_(k+1) .. . Ω*_(k+m) Ω*_(k+m+1) . . . Ω*_(k+m+j)

The amplitude-sorted components of the base Zyoton can be grouped intohigh, medium, and low-energy components (i.e., k, m, and j components)according to the amplitudes thereof. The boundaries between thehigh-energy and the medium-energy components and between themedium-energy and low-energy components are not absolute, and canchange, depending on the embodiment. Thus, the designations of one ormore frequency components to a particular group can change.

Using the value of k, computed, e.g., as described with reference toFIG. 39, the first k components of the base Zyoton, i.e., the components{<A*₁, Ω*₁>, . . . <A*_(k), Ω*_(k)>} may be selected to be included asthe high-energy k components in the Zyoton to be synthesized. Using thevalue of m, computed, e.g., as described with reference to FIG. 40, thefirst m components of the base Zyoton from the medium-energy groupthereof, i.e., the components {<

>, . . . , <

>} may be selected to be included as the medium-energy m components inthe Zyoton to be synthesized. Similarly, using the value of j, computed,e.g., as described with reference to FIG. 41, the first j components ofthe base Zyoton from the low-energy group thereof, i.e., the components{<

, . . . <

>} may be selected to be included as the medium-energy m components inthe Zyoton to be synthesized. In general,

>k;

>m; and

>j.

In some embodiments, the amplitudes A(i) of the Zyoton thus formed,require no further adjustment. In other embodiments, however, theamplitudes of these components, initially set to be A*_(i) according tothe selected components of the base Zyoton, are adjusted in step 10.These adjustments may be performed according to the ratio of theaverage, median, minimum, or maximum magnitude of the second derivativein the regions that correspond to high and low analyte absorptionwavelength regions. To this end, the pure component spectrum XA of theanalyte of interest is partitioned into a number of wavelength regions,where each wavelength region corresponds to a particular range ofwavelengths [λ₁, λ₂] of the spectrum XA. The wavelength regions are thussimilar to features but, in general, features correspond to wavelengthregions of the spectral signals obtained from a medium to be analyzed.The wavelength regions described herein are generally derived from purecomponent spectra.

Some of these wavelength regions, where the absorption of energy by theanalyte of interest is high are designated as analyte wavelengthregions. Some wavelength regions, where the absorption of energy by theanalyte is low, are designated as non-analyte wavelength regions. Theterms high absorption of energy and low absorption of energy should beunderstood in the context of analysis, as described above. One or moreof the several analyte wavelength regions are selected to interact (viaconditioning thereof) with the Zyoton and the carrier kernel to besynthesized. The number of the selected analyte wavelength regions is n.Each of these n selected analyte wavelength regions is denoted Fi, andis paired with a corresponding non-analyte wavelength region denotedNFi, forming n wavelength region pairs FP.

For each wavelength-region pair FPi, two regions of the secondderivative of XA, i.e., XA″, are identified, where the first region ofthe second derivative corresponds to the wavelength boundaries of Fi,i.e., [λ_(1i), λ_(2i)], and the second region of the second derivativecorresponds to the wavelength boundaries of NFi. A ratio Ri of theaverage, median, minimum, or maximum magnitude of the first region ofthe second derivate to the average, median, minimum, or maximummagnitude of the second region of the second derivative is thencomputed. These steps are performed for each of the n wavelength-regionpairs, to obtain n ratios. The maximum and minimum of these ratios,denoted R^(max) and R^(min) are then computed.

The amplitudes of the k Zyoton components, i.e., the high-energy oranalyte-information representing components, are then selected such thatthe pair-wise ratios thereof are distributed in the range [R^(max),R^(min)]. In particular, if the amplitudes of the k Zyoton componentsare [A1, A2, . . . , Ak], A1 is designated a specified value, e.g.,(1,000; 1,600; 4,000; 10,000; 50,000; 125,000, etc.). In someembodiments, the value of the amplitude A*₁ of the base Zyoton may beretained. A2 is then selected such that A1/A2=R^(max). An intermediateratio value R2 less than R^(max) but greater than R^(min) is thenselected, and A3 is selected such as A2/A3=R2. Another intermediateratio value R3 less than R2 but greater than R^(min) is then selected,and A4 is selected such as A3/A4=R3. The amplitudes of the k Zyotoncomponents are thus selected such that, finally, the ratioA(k−1)/Ak=R^(min). In some embodiments, the ratios are distributed inthe ascending order, in the range [R^(min), R^(max)]. In variousembodiments, the distribution of ratios, i.e., the selection of theintermediate ratios R2, R3, etc., can linear, quadratic, or exponential,for example.

In various embodiments, the amplitudes of the j frequency components,i.e., the non-analyte-information representing components, may beselected randomly as a fraction (e.g., in a range from about 1/100 to1/1000^(th)) of the amplitude of any of the k Zyoton components. In someembodiments, the amplitudes of the j components can be a percentage suchas 2%, 5%, 10%, 50% of the amplitudes of the k components. Theamplitudes of the m transition component can be a multiple (e.g., 2, 3,5, 10, etc.) of the amplitude of any of the j Zyoton components. The(k+m+j) frequency components may then be sorted by amplitude in step 12.In the time domain, a Zyoton thus constructed is a traveling waveformthat can be perturbed if collided with another waveform such as anunmodulated carrier kernel or a conditioned feature. The perturbationgenerally results in a change in the morphological profile of theZyoton, e.g., a change in dispersion velocity, divergence, etc. Withouta collision with another waveform, however, the Zyoton can propagatesubstantially unperturbed, i.e., without a substantial change indispersion velocity, divergence, etc., at least over a preselecteddistance, such as the length of a collision grid (e.g., 2000 points;10,000 points; 20,000 points; 100,000 points; or more) in the timedomain. Substantial in this context can be a more than 0.001%, 0.005%,0.02%, 0.1%, 1%, 5%, 10%, 20%, etc. change in a parameter of interestsuch as dispersion velocity over the distance of propagation.

The frequency components of the carrier kernel may be selected tocorrespond to those of the Zyotons in step 14. In general, theamplitudes of the k, m, and j components of the carrier kernel areselected such that the spectral energy of the carrier kernel is only afraction (e.g., 1/100, 1/1,000, etc.) of the spectral energy of theZyoton. In some embodiments, the amplitudes of the frequency componentsof a Zyoton are determined as described above, and then the amplitudesof the corresponding frequency components of the carrier kernel are setusing a constant scaling factor such as 0.25, 0.2, 0.1, 0.08, 0.03,0.01, etc.

In some embodiments, the scaling factor is selected such that the Zyotonand the unmodulated carrier kernel are co-dependent. This can beachieved by applying a Kappa test to these two waveforms. In particular,if a magnitude of a difference between a scaled velocity of the Zyotonand the velocity of the carrier kernel is not greater than the value ofa Kappa parameter κ_(SYN), used during synthesis, the Zyoton and thecarrier kernel are likely co-dependent. The co-dependence typicallycannot be ascertained during waveform synthesis because a conditionedfeature obtained by modulating the synthesized carrier kernel with oneor more features, and used in a collision operation, typically has adifferent energy and velocity than that of the carrier kernel.

In various embodiments the parameter κ^(SYN) is similar to the parameterκ_(DV2) discussed above. In performing the above-described Kappa test,the velocity of the unmodulated carrier kernel may be scaled during thecomparison, instead of or in addition to scaling the velocity of theZyoton. The Kappa test using the parameter κ^(SYN) can be performed inthe time domain or in the frequency domain. If this Kappa test fails,the frequency-domain amplitudes of the frequency components of theZyoton, the carrier kernel, or both, may be scaled using a scalingcoefficient α_(SYN), which is similar to the normalized scalingcoefficient α_(C) discussed above, such that the Kappa test wouldsucceed using the adjusted Zyoton and/or the carrier kernel.

An example of some of the frequencies and amplitudes in a carrier kernelfor the k, m, and j components is shown in Table 7 below.

TABLE 7 Frequency Frequency Component Amplitude Region (KHz) (dBm/Hz) K218.7 625.4878 277.4 260.5532 317.2 233.3075 123.4 233.3075 87.16194.6868 412.9 194.6868 M 497.3 38.5267 511.1 38.5267 732.42 35.9625614.9 35.9625 507.2 33.6208 843.1 33.6208 328.6 25.5264 J 1832.4 6.38167322.1 5.0936 5376.2 5.0936 11236.5 4.0355 9032.5 4.0355 18043.1 3.82077344.5 3.8207 11264.4 2.5359 14090.2 2.5359 9433.7 1.2619 . . . . . .

In the table above, the first six frequency components are the kcomponents, the next seven components are the m components, and the restare a subset of the j frequency components. To design a carrier kernel,a desired amplitude profile for the k, m, and j components is set. Theexample relationship among the amplitudes described here, assigned totheir respective frequency components, was established for an embodimentof glucose measurement, such that all the frequency components interactand mix with the selected Zyoton. A function generator and/or a waveformsynthesizer can generate the carrier kernel from the frequencycomponents selected as described above. The carrier kernel is thenmodulated using the feature waveform to obtain a correspondingconditioned feature. In some embodiments, a time-domain representationof the carrier kernel is discretized into a selected number (e.g., 2048)of points.

A feature as extracted from an absorbance spectrum may be initiallyrepresented as a 32 point waveform. FIG. 32 shows an absorbance profileof a single feature, extracted from a reflectance intensity spectrum inthe region between 6493 cm⁻¹ (1540 nm) and 6433 cm⁻¹ (1554 nm). Theinitial feature length here, as extracted from an absorbance spectrum,is 32 data points (60 cm⁻¹) for a resolution of the spectrum of 2 cm⁻¹(including the two endpoints of the spectral range). In variousembodiments, that feature waveform is up-sampled to the length of thecarrier kernel (e.g., 2048) using e.g., spline interpolation to matchthe length of the two waveforms. FIG. 42 shows the feature absorbance ofFIG. 32, up-sampled by interpolation to 2048 data points from theinitial 32-data point spectral feature. This up-sampling may be done tomatch the length of the carrier kernel and Zyoton waveforms, and isfollowed by the optional precursor frequency modulation described above.Features can be obtained from reflectance/intensity signals and thensuch features can be transformed into absorbance-representing features.Alternatively, as described above, the reflectance/intensity signal canbe transformed into an absorbance signal and the features can beobtained therefrom.

A Fourier transform is then applied to the up-sampled and optionallymodulated feature (also called a feature vector) to obtain a Fouriertransformed feature. FIG. 43 shows an example of the first 10 frequencycomponents associated with the up-sampled feature shown in FIG. 42. AFourier transform of the carrier kernel is also generated to obtain aFourier transformed carrier kernel, which includes the k, m, and jfrequency components, as described above. In some embodiments, theFourier transformed feature and carrier kernel are convolved to obtain aFourier transformed conditioned feature waveform. In some embodiments,the carrier kernel is frequency and/or phase modulated by the originalor up-sampled feature, to obtain the conditioned feature. Thismodulation can be performed in the time (wavelength) domain or in thefrequency domain. If the modulation is performed in the frequencydomain, a time-domain representation of the conditioned feature waveformcan be generated using the inverse Fourier transform of thefrequency-domain representation of the conditioned feature, e.g., theresult of a convolution of the Fourier transformed carrier kernel andthe Fourier transformed up-sampled feature.

In various embodiments, the co-dependency between a Zyoton and aconditioned feature to be collided therewith is achieved by ensuringthat: (i) an absolute difference between their respective dispersionvelocities is less than a specified threshold κ_(DV2), and (ii)divergence of the envelopes of a selected number of sidebands of themodified Zyoton created as a result of a collision is less than anotherspecified threshold τ. As described above, the first condition can betested prior to a collision between the original Zyoton and theconditioned feature, using the constraint variable κ_(DV2).Additionally, or in the alternative, the first condition may be testedpost collision, between the original Zyoton and a modified Zyoton usingthe constrain variable κ_(DV3), or between the original Zyoton and arenormalized Zyoton, using the variable κ_(DV1). It should be noted thatwhile κ_(DV1), κ_(DV2), κ_(DV3), and τ may optionally take on differentvalues, they all serve to enforce the co-dependency conditions.

The first type of constraints, κ_(DV1), κ_(DV2), and κ_(DV3), arerelated to the dispersion velocity, which can be represented in the timedomain as the amplitudes of the selected sideband peaks of thetime-domain representation of the waveforms considered, as discussedabove. In the frequency domain, the dispersion velocity can berepresented by the amplitudes of the first k frequency components or, asdescribed above, by (∥A′_(k)∥−∥A_(k)∥). The second type of constraint,τ, is related to the divergence of the sideband envelopes which may becaused by the introduction of new m and/or j frequency components in thepost-collision modified Zyoton—which can result in a subtle change inthe morphology (e.g., the overall shape) of the modified Zyoton.

In general, the dispersion velocity can be described as the velocitywith which the narrow-band peak envelope of a Zyoton (e.g., thestrongest peak of the underlying soliton kernel as shown in FIG. 12A)propagates in a medium over time, ignoring higher order chromaticdispersion and nonlinear effects such as those arising from thepropagation of lower amplitude pulses (or higher frequency components)in the Zyoton. Chromatic dispersion of the Zyoton generally results fromthe introduction of new m and/or j frequency components and thenonlinear effects from changes in the amplitudes of the m and/or jfrequency components.

Energies associated with peaks at these new frequencies can distort theshape of the waveform. The computation of dispersion velocity ofsolitons, which can be used to analyze Zyotons, is discussed in Haus andIppen, “Group velocity of solitons,” Optical Letters 26 (21), 1654(2001), the entirety of which is incorporated herein by reference.

Changes in the post-collision dispersion velocity, i.e., the dispersionvelocity (or the velocity) of a modified Zyoton can be constrained bythe asymmetric energy relationship between the conditioned featurewaveform and the Zyoton waveform, or between the renormalized Zyotonwaveform from the previous iteration and the Zyoton, as described above,where the energy of the Zyoton may be three or more orders of magnitudemore than that of the conditioned feature and/or the renormalizedZyoton. In various embodiments, the conditioned feature waveform and therenormalized Zyoton can be scaled (as described below in the collisionequation) to a small fraction of the total spectral energy of theselected Zyoton, in order to achieve the desired energy balance.

As described above, the introduction of additional m and/or j frequencycomponents can change the shape of the modified Zyoton relative to theshape of the original Zyoton. This shape divergence can be described asa change in the width of the post-collision Zyoton waveform envelope.FIGS. 14A-14B are time-domain representations of a Zyoton and a modifiedZyoton resulting from a collision of the Zyoton and a conditionedfeature. FIG. 14A shows that the time-domain length of the originalZyoton is

and FIG. 14B shows the time-domain length of the modified Zyoton is

₁. The post-collision, pre-renormalization time-domain length of themodified Zyoton can be stated as

₁=

+Δl₁, where Δl₁ is the width of divergence after the first collision. Inorder for the collision to be nearly elastic, Δl₁ is required to be lessthan a specified threshold τ. An example of a numerical value of τ is

/100.

The renormalization can change the width of the modified Zyoton suchthat the width of the renormalized Zyoton is reset to

. Such renormalization can be achieved via truncation and/or re-samplingin the time domain. If the modified Zyoton is represented in thefrequency domain, re-sampling can be implemented by performing aninverse Fourier transform of the frequency components of the modifiedZyoton, followed by truncation and/or down-sampling, to adjust the widthof the modified Zyoton. Then a Fourier transform followed by anamplitude sort of the frequency components can establish the amplitudesthat may be used to obtain the renormalized Zyoton. The co-dependencycondition requires that the amplitude vectors described above and/or thecorresponding frequency components be selected during the synthesis ofthe Zyoton and the carrier kernel such that conditions described abovein terms of the thresholds κ_(DV1), κ_(DV2), κ_(DV3) and τ aresatisfied.

Formation of Conditioned Features

The process for ensuring co-dependency is related to the process ofsynthesizing a carrier kernel, as described above, and to the process ofgenerating one or more conditioned features. FIGS. 44A and 44Brespectively show the distribution and a detailed profile of basefrequencies used in the synthesis of one carrier kernel. FIG. 44A showsthe plot of amplitudes of base sinusoidal frequencies as a function of afrequency index, that can be used to generate the carrier kernel. FIG.44B illustrates the distribution of the first 16 frequency components asan example. A frequency index is created by sorting the frequencycomponents on the basis of the amplitudes of their Fourier components.

In one embodiment, pure-component spectra of the analyte of interestover the wavelengths of interest are deconstructed into spectralfragments (also referred to as wavelength regions or spectral regionsof). The boundaries of these spectral fragments generally correspond tothose of spectral features to be used to generate conditioned featuresusing the carrier kernel. The pure-component-spectra-based spectralfragments can be used to determine the values of one or more Kappaparameters described above. To this end, interpolation and/or pre-cursormodulation are optionally applied to the spectral fragment. A carrierkernel is modulated using the spectral fragment to obtain a conditionedfragment. The conditioned fragment is collided with a Zyoton, and achange in dispersion velocity of the modified Zyoton relative to thedispersion velocity of the original Zyoton is computed.

Noise such as randomly generated gray noise with a correlation time of10⁻⁶ seconds may then be added to the spectral fragment. The amount ofnoise can be a fraction of (e.g., 2%, 25%, 50%, etc.), equal to, or amultiple of (e.g., 2, 5, 10, 100, 1000, 10000 times, or more) theexpected and/or measured noise of the non-invasive measurement system.The above-described steps may then be repeated using the noisy spectralfragments to obtain corresponding changes in the dispersion velocity ofthe modified Zyoton. The steps of adding noise, generating a conditionedfragment, colliding it with a Zyoton, and computing a change in thedispersion velocity may be repeated for different amounts of noise. Theparameter κ_(DV1) may then be set according to these observed changes.For example, κ_(DV1) can be a minimum, average, median, or maximum ofdifferent observed changes in the dispersion velocity. Other Kappaparameters discussed above can be set relative to κ_(DV1).

FIGS. 45A through 45D illustrate the distribution of amplitudes ofcarrier kernel frequencies and their frequency components in the timeand frequency domains. The profile of the full carrier kernel and azoom-in to the high-amplitude frequency components are shown. FIG. 45Ashows the time domain representation of a carrier kernel waveformgenerated using the frequencies shown in FIG. 44A. FIG. 45B provides adistribution of carrier kernel waveform frequency components,specifically a distribution of the amplitudes of these components, as afunction of spatial frequency. FIG. 45C shows a time-domainrepresentation of the waveform shown in FIG. 45A, down-sampled to 2048data points. The down-sampling is optional and a down-sampled waveformmay include less than 2048 (e.g., 2000, 1024, 1000, 600, 512, 200, etc.)or more than 2048 (e.g., 3000, 5000, 10,000, 40,960, etc.) points. FIG.45D shows the distribution of the spatial frequencies of thedown-sampled carrier kernel waveform and amplitudes of the frequencycomponents as a function of spatial frequencies.

In ordinary frequency modulation (FM), a signal modulates the frequencyof a carrier wave where the modulated output does not have any nonlineardependence on the original signal. In various embodiments describedherein, the carrier kernel is frequency modulated by a feature. Thecarrier kernel is created with several selected frequencies, and theresult of modulation by the feature creates a nonlinear relationship tothe feature. A non-linear relationship is achieved because the carrierwave is a summation of several frequencies instead of a single one.Other types of modulation, e.g., amplitude modulation, phase modulation,etc., and/or combinations of two or more modulation techniques can beused to modulate a carrier kernel using a feature.

In general, a carrier kernel includes a set of distinct carrierfrequencies F _(c)=[f_(c1), f_(c2), . . . , f_(cN) _(K) ], where N_(K)is the number of component carrier frequencies in the kernel.Optionally, there are several harmonics of each frequency f_(c1) embededin the carrier kernel. As stated above, the feature data extracted froma spectrum has low spatial frequency content, generally due to a limiteddata vector length of the feature. This spatial frequency content isoften insufficient to characterize changes in the feature properties dueto low analyte concentration and interference from confounders. Couplingthe feature with a complex carrier kernel with a high spatial frequencycontent, after an optional precursor modulation, can provide additionaldegrees of freedom to characterize the underlying analyte. Differentfeatures, associated with different wavelength regions, with differentunderlying analyte concentrations and corresponding absorption ofenergy, modulate the carrier kernel differently. When the carrierkernel, modulated by the feature (and thus transformed to a conditionedfeature) with an expanded range of spatial frequencies, is collided withthe Zyoton (which also has an expanded range of corresponding spatialfrequencies), the analyte absorption properties can be extracted andamplified. In some embodiments, the same carrier kernel is used for allfeatures, regardless of the wavelength regions from which those featuresare derived. Different carrier kernels and/or different Zyotons can beoptionally used for different features.

A set of carrier frequency component amplitudes C=[C₁, C₂, . . . , C_(N)_(K) ] is associated with F _(c). As described above in the discussionof Zyoton and carrier kernel synthesis, the choice of the frequenciesf_(ci) for i=1, . . . , N_(K), and N_(K) relate to the relationshipbetween absorbing and non-absorbing feature wavelength regions in theFourier transform of the analyte's pure component spectrum, and/or noisecharacteristics of the feature, and by the anticipated confounderinterference, as expressed by the SCR. Specifically, the selection of atleast some of the carrier kernel frequency components was describedabove, relating them to the number of components of afrequency-component based discriminant classifier required to overcomethe introduced distortion of the second derivative of the pure componentspectrum for an analyte of interest in the presence of confounders andadded random noise. All the frequency components and their amplitudescan be provided to a signal generator or synthesizer to generate thecarrier kernel waveform.

Spectral features need to be appropriately prepared before modulating acarrier kernel by those features. FIGS. 46A through 46C show a featureprepared in the absorbance domain and the distribution of spatialfrequencies and their amplitudes in sorted order. In particular, FIG.46A shows the absorbance spectrum of a feature, which can obtained bytransforming an intensity spectrum obtained from a sensor, as describedbelow. FIG. 46B shows all frequency components of the feature in theamplitude-sorted order, and FIG. 46C shows the first ten frequencycomponents of the feature in the amplitude-sorted order.

When a carrier kernel is modulated by a feature waveform, a Fouriertransform of the resulting conditioned feature typically includes morethan N_(K) frequency components. In general, the modulated carrierkernel, i.e., the conditioned feature includes (k+m_(CF)+j_(CF))frequency components. The first k frequency components represent theenergy absorbed by the analyte and/or one or more confounders. Theamplitudes of these frequency components are denoted a_(k), a_(m) _(CF)and a_(j) _(CF) , as depicted in FIG. 11. The Zyoton with which theconditioned feature is collided generally includes (k+m_(Z)+j_(Z))frequency components, and the amplitudes of the frequency components ofthe Zyoton are denoted A_(k), A_(m) _(Z) , and A_(j) _(Z) , as alsodepicted in FIG. 11. The respective frequency components of the Zyotonand the conditioned feature, however, need not have exactly the samefrequencies.

FIGS. 47A through 47D illustrate the distribution of frequencies and thenormalized amplitudes of the frequency components of a conditionedfeature after modulation of the waveform by a feature. All of thefrequency components of the conditioned feature waveform, sorted byamplitude, are shown in FIG. 47A. The analyte-information-representing kcomponents of the conditioned feature are shown in FIG. 47B. FIG. 47Czooms in to the transition zone or mid-amplitude range m components ofthe conditioned feature, and FIG. 47D zooms in tonon-analyte-information representing j components of the conditionedfeature. FIGS. 48A and 48B show a time-domain representation of theconditioned feature having a frequency domain profile shown in FIGS. 47Athrough 47D. A zoom-in to the overall time-domain profile of theconditioned feature waveform from FIG. 48A is shown in FIG. 48B.

FIGS. 12A through 12C show the morphological profile and amplitudeenvelopes of an example one-dimensional Zyoton, derived from solitons,and corresponding to the Zyoton_D1 (shown in FIG. 49). FIG. 12A shows atime-domain representation of the Zyoton and FIG. 12B shows a zoomed-inrepresentation of the Zyoton. FIG. 12C shows the primary peak in thetime domain, and selected b sideband peaks on both sides of the primarypeak. FIGS. 50A through 50C show time-domain representations of otherZyoton waveforms that may be used in collision computing. Specifically,these Zyotons waveforms correspond, respectively, to Zyoton D3, ZyotonD1, and Zyoton MM1 (shown in FIG. 49).

FIGS. 51A through 51C show the frequency domain representation of thedifferent Zyoton waveforms, i.e., Zyoton_D1, Zyoton_D3, and Zyoton_MM1.These frequency-domain representations correspond, respectively, to thetime-domain representations shown in FIGS. 50A through 50C. FIG. 51Dshows a zoom-in to the frequency components of Zyoton_MM1. FIGS. 52Athrough 52C show the profile of amplitude-sorted frequency componentsfor the Zyoton waveforms Zyoton_D1, Zyoton_D3, and Zyoton_MM1,respectively.

In various embodiments, the parameters δ and φ (as described below inthe collision equation), are applied to the Zyoton and/or conditionedfeature waveform vectors. In various embodiments, for computationalefficiency, Zyotons are expressed as one-dimensional traveling waves inthe x, y or z dimension over time. The Zyotons may be synthesized,however, using complex-valued waveform families (e.g., solitons) and/orgenerator functions that are plane-wave, i.e., two-dimensionalconstructs (having x and y dimensions over time), or eventhree-dimensional constructs (having x, y, and z dimensions over time).As the corresponding Zyotons may be represented as one-dimensionaltraveling waveforms, a compensating mechanism may be employed for thisdimensional simplification between Zyotons and the travel models of thewaveforms from which they are derived. As an example, a general form ofa two-dimensional soliton plane wave is S(x, t)=Ae^(iρ)e^(i(kx-ωt)),where A is a positive constant called the amplitude, ρε[0, 2π) (whichsymbolizes that ρ can vary from 0 to 2 π) is called the initial phase, kand ω are two real-valued parameters called the wave number and theangular frequency, and

$\frac{k}{2\pi}$is the number of waves per unit length, while

$\frac{\omega}{2\pi}$is the number of waves per unit time. For one-dimensional Zyotons, thedispersion velocity along the propagation axis is expresses as

$\frac{\omega(k)}{k}.$

In various embodiments, the collision operation is notionallyone-dimensional, but the complete collision operations may need to beplanar or three dimensional. Therefore, a phase rotation operation cancapture the phase distribution effects. In some embodiments, a totalphase rotation space of 2 π is set for the entire collision process. Thetotal 2 π phase rotation is then divided by the number of collisioniterations, to compute the rotation on a per collision iteration basis.This can compensate for the random variability in the collision processthat may result from restricting the collision operation to a singledimension.

The power spectral density profile of the unscaled Zyoton (Zyoton_D1) isshown in FIGS. 53A-53B. An amplitude-sorted frequency component profileof a conditioned feature to be collided with Zyoton_D1 as shown in FIG.53C. FIGS. 54A through 54C respectively show amplitude time-domainprofile, frequency distribution, and power spectral density profile ofZyoton_D1 waveform, prior to a collision. The scaling coefficient α_(z)was used match the spectral energy ratio of the Zyoton waveform to thespectral energy of the conditioned feature as described above. FIGS. 55Aand 55B show the amplitude-sorted frequency component profile of amodified Zyoton waveform obtaining by colliding the scaled Zyoton_D1with the conditioned feature described with reference to FIG. 53C. Azoom-in to the amplitude-sorted frequency component profile of themodified Zyoton is shown in FIG. 55B.

Construction of the Collision Operator

With reference to FIG. 56, in various embodiments, one or more ofcertain specific analysis objectives, 2 a, 2 b, 2 c, 2 d, and 2 e areused for the selection of waveform families and/or waveform generatorsto be used in Zyoton and/or carrier kernel synthesis, and/or in thesynthesis of Zyoton and/or carrier kernel waveforms. One or more ofthese objectives may also be used in selecting parameters forconditioning the extracted features, and the parameters defining theprocess of collision computing. The analysis objectives include: analytedetection sensitivity, i.e., how small a change in analyte quantity isrequired to be detected, the output concentration precision, and theaccuracy of measurement with respect to a reference standard for theanalyte.

One or more sensor parameters, such as resolution, sampling interval,dynamic range, sensor bandwidth, and the expected clutter absorption(i.e., expected signal-to-clutter ratio (SCR) increase that isrequired), may also be used for Zyoton and carrier kernel synthesisand/or in the selection of collision parameters and configuration of thecollision computer. The specific Zyoton waveform selection depends onthe expected required signal-to-clutter increase and the overlap betweenthe signal and clutter observables. Both magnitude and shape similaritybetween the analyte and the confounders overall may drive the selectionof the waveform families and/or generator functions used in Zyotonsynthesis, as described above.

One or more of the sensor resolution, drift, precision, and noisecharacteristics may be used to set the number of frequency components ofthe synthesized Zyoton waveform to be used in the spectral energycomputations as well as the number of frequency components of thecarrier kernel waveform used for feature conditioning. The relativescale of peak energy of the Zyoton waveform and its co-dependentconditioned feature waveform are used in the determination of thescaling coefficients and scaling vectors for the conditioning processand for the collision process. The number of collision iterationsrequired is generally proportional to the expected required SCRincrease. In some embodiments, the number of collision iterations may beincreased by a partial or full order of magnitude for each order ofmagnitude increase in the expected required SCR.

The number of collisions (also referred to as collision count parameter)may be set depending on the sensor signal-to-noise characteristics. Insome embodiments, the number of collisions is initially set to 100 whenthe signal to noise ratio (SNR) of the sensor is 1000:1. As an example,the SNR of a spectroscopic standard can be determined by the ratio ofpower of a selected band (e.g. a 1 nm band) at a wavelength of interest(e.g., 1650 nm) to the ratio of background power in the same band usingan NIR Diffuse Reflectance Standard with known reflectance value. Thecollision count parameter may be altered during calibration of thecollision computer to accommodate sampling variability. The number ofcollisions is generally increased by an order of magnitude if the SNR ofthe sensor or SCR decreases by an order of magnitude. For example, in anembodiment for non-invasive glucose measurement in tissue, with SCR of10⁻⁴, a collision count of 20,000 was used with a sensor SNR of 10³. Ina similar manner, the number of collisions can be decreased if the SNRand/or SCR were to increase. The minimum number of collision iterationsrequired is one. In various embodiments, the expected required SCRincrease is determined by analyzing expected overlap and energyabsorption due to dominant confounders which have spectroscopicabsorption peaks in the same region as the analyte in the spectralbandwidth where the spectrum is acquired.

As described above, the specific properties of the collision processthat are selected to estimate accurately the presence, absence,concentration, and/or rate of change of concentration over a fixed timeinterval (e.g., in seconds or minutes) of an analyte include theselection (or synthesis) of the collision waveform or Zyoton 10, whichdepends, at least in part, on the expected required SCR increase. Thisincludes the selection of a base family of usable waveforms and thesetting of one or more Zyoton parameters during synthesis thereof.Selecting the collision parameters, 20, includes selecting the number ofcollision iterations to be performed to assess the net absorption ofenergy due to the analyte of interest, and setting the collisionoperator, i.e., the delay shift, scaling, and phase adjustmentparameters. The interaction between the frequency components of aconditioned waveform and a co-dependent Zyoton waveform generallyprovides a robust estimate of energy changes due to selective energyabsorption by the analyte. In some embodiments, the net energy change isan energy gain in successive collision iterations. The collisioncomputer can be configured and the colliding waveforms can beconstructed such that the energy change in successive collisioniterations is an energy loss.

In general, the collision between a Zyoton and a conditioned feature orbetween a Zyoton and a renormalized Zyoton resulting from the previouscollision iteration creates a finite-range frequency componentperturbation. As scattering due to the medium is inherently random, butstatistically bounded in time and space, in some embodiments, Zyotonwaveforms are selected that are soliton-based and which show absorptioneffects more strongly in the analyte-information representing kfrequency components, which in some embodiments are high-amplitudecomponents. The scattering effects are generally represented morestrongly in non-analyte information representing j frequency components,which in some embodiments are low-amplitude components. The total set offrequency components of the Zyoton is described as H=k+m+j where k>0,m≧0, and j>0, and k and j frequency components generally do not overlap.

Such a Zyoton waveform can be constructed, as described above, using thepure component spectra of analytes (such as glucose) and pure componentspectra of one or more confounders, including dominant confounders, andby modeling the scattering effects, if any, of the medium to beanalyzed. The wavelength dependent absorption and scattering propertiesof the medium may be modeled in order to synthesize the Zyotons andcarrier kernels to be used in the collisions. This knowledge frombio-optical models and chemistry generally yields suitable waveformfamilies and generator functions for synthesizing Zyoton waveforms, andcan also guide the number of frequency components that are used in theestimation of analyte-specific absorption energy.

Once the number of frequency components that can yield a robust estimatefor analyte-specific absorption is established for theanalyte-information representing (i.e., k), transition (i.e., m), andnon-analyte information representing (i.e., j) regions of the Zyoton andcarrier kernel waveforms, (e.g., k=6, 7, 10, etc., in some embodimentsfor non-invasive glucose measurement), the parameters of the collisiongrid can be computed. In addition, for computational efficiency and tolimit the computer memory requirements, windowed and/or bracketedinteractions may be used to implement the waveform collisions.

In various embodiments, the window length is set such that interactionof frequency components that are used in the computation of spectralenergy changes due to the analyte-specific spectral absorption can bepropagated from one collision to the next. In some embodiments, thewindow length is set such that the frequency component changes resultingfrom scattering effects are substantially eliminated during thetruncation operation built into the collision process. In someembodiments, variations in the scattering properties of the medium maycontain analyte information and, as such, at least some frequencycomponents corresponding to the scattering properties of the medium maybe retained. The renormalization performs a truncation according to thewindow length. Optionally, the collision parameters can be altered, 30,during the collisions. Specifically, one or more properties of Zyotonsmay be modified and the constraints or boundary conditions for thecollision operation, e.g., the Kappa parameters described above, may bemodified, to ensure that each collision is a valid interaction.

The overall process of constructing a collision computer can besummarized as follows: (a) Frequency components of the second derivativeof a signal generated from pure component spectra, or frequencycomponents of the pure component spectra themselves or of the first orother higher order derivatives of the pure component spectra, with addedrandom noise may be used to determine the numbers (k, m, and j) offrequency components of the carrier kernel; (b) The same analysis can beused to determine the numbers (k, m, and j) of frequency components ofthe Zyoton, as well; (c) The spectral properties (e.g., bandwidth,morphology, etc.) of the signals and/or frequency components in step (a)above can be used to select a suitable Zyoton family; (d) The frequencyof the peak component of the Zyoton can be any frequency within thefamily that supports the bandwidth of the signals and/or frequencycomponents; (e) Frequencies of other Zyoton components can be selectedaccording to the numbers k, m, and j.

Moreover, (f) Frequencies of the frequency components of the carrierkernel in some embodiments must match respective frequencies (e.g.,within a value σ, where σ is defined as:

$\left. \frac{BW}{2\left( {k + m + j} \right)} \right)$of the corresponding Zyoton components, where BW is the bandwidth of thecarrier kernel (in Hz) and k, m and j refer to the number of frequencycomponents of the carrier kernel as described above; (g) The amplitudesof the frequency components of the Zyoton and the carrier kerneldetermine the relative spectral energies of the Zyoton and the carrierkernel. (h) The amplitudes of the respective time-domain waveformscorresponding to the frequency components determine the respectivevelocities of the Zyoton and the carrier kernel.

During the collision iterations, truncation of a modified Zyoton, i.e.,the removal of one or more frequency components of the modified Zyotonduring the post-collision renormalization may cause the renormalizedZyoton (which is typically the “feature proxy” for the next collision),to be clipped. The amplitudes of the surviving components of therenormalized Zyoton frequency components are generally rescaled toreintroduce the effect of this clipping. In various embodiments,renormalization performs the rescaling (also called amplitudebalancing).

Some Zyotons, however, have severe nonlinearities and such rescaling isdifficult to apply to a modified Zyoton. Therefore, in some embodiments,the rescaling is applied to the original Zyoton waveform instead, tooffset the clipping of the modified Zyoton that was performed to obtainthe renormalized Zyoton, which is then collided with the original Zyotonas rescaled, in the next collision iteration. This may allow for aconsistent, repeatable correction to be applied in each collisioniteration, so as to ensure the co-dependency of the colliding waveforms.Truncation of the modified Zyoton (and downscaling thereof to remove theenergy of the original Zyoton), to obtain a renormalized Zyoton, and amodification of the original Zyoton instead of amplitude rebalancing ofthe renormalized Zyoton, can improve the computational efficacy of thecollision process and/or may reduce latency in producing the result forreal-time analysis of sensor data.

In some embodiments, e.g., for glucose detection, the Zyoton propertiesare not changed between collisions, i.e., the same Zyotons are used. Thecollision operator is also not altered. In some configurations of thecollision computer, however, the collision operator may be modifiedafter each successive collision for certain applications. The selectionof the parameters as described above generally specifies the collisioncomputer 50.

As a Zyoton represents a traveling wave, its instantaneous amplitudecoefficients (i.e., the absolute value of the magnitude of amplitudepeaks as a function of different frequencies in the envelope of thewaveform at a particular time where the envelope function of wave has asmooth curve outlining its extremes, as shown in FIGS. 12A-12C serve asinitial conditions for analyzing propagation behavior through apropagation medium over time. In various embodiments, the Zyotons aresynthesized such that numerical differences in propagation propertiesbefore and after collision are small and propagation of the Zyotonremains substantially unchanged in terms of the dispersion velocity anddivergence thereof.

To ensure that Zyoton properties are preserved, i.e., the Zyoton isperturbed but only within certain limits, the post-collision velocity ofthe modified Zyoton is compared to that of the original Zyoton. Unlessthe difference is within a given threshold κ_(DV3), the original Zyotonand the modified Zyoton are not acceptable for additional collisions,and the collisions are not “nearly elastic,” as described above. In someembodiments, the modified Zyoton is renormalized and the velocities ofthe original and renormalized Zyotons can be compared to ensure that thedifference therebetween does not exceed the threshold κ_(DV1). Inaddition, it is also tested whether divergence of the modified Zyoton isnot greater than the threshold τ. If the kappa and tau tests are bothmet, the collision is determined to be nearly elastic, and theperturbation of the Zyoton is determined to be within limits specifiedby the kappa and tau parameters. In some embodiments, the collisionoperator is constructed such that the divergence test need not beperformed explicitly. In various embodiments, the velocity anddivergence tests may be performed in the time domain and/or in thefrequency domain and, accordingly, the various kappa and tau parametersmay take on suitable values.

If the velocity difference and/or the divergence are outside therespective thresholds, the Zyoton may be sub-optimal as a collisionentity. A new Zyoton may then be selected or synthesized, or the featuredata may have a gross artifact and may be examined. One or more newfeatures may be obtained from additional samples.

In some embodiments, in addition to selecting/synthesizing Zyotons andcarrier kernels and configuring the collision computer, the extractedfeatures are conditioned for collisions using the process shown in FIG.37. In particular, in some embodiments, a selected feature 4 ismodulated in step 10 using a signal such as 16.5 Hz, 30 Hz, 75 Hz, 125Hz, 500 Hz, 1 kHz, 40 kHz, 100 kHz, 260 kHz, 1 MHz, or a signal havingeven higher frequency. This modulation in step 10, called precursormodulation, is optional. The precursor modulation can be amplitude,frequency, or phase modulation or a combination of any two or all threeof these. Alternatively, or in addition, in some embodiments, thefeature is interpolated at step 10, to match its time-domain length withthat of the carrier kernel. The interpolation of the feature is alsooptional. The feature (which may be pre-cursor modulated and/orinterpolated) is used to frequency modulate a carrier kernel at step 30,to turn that feature into a conditioned feature. To this end, frequencymodulation is performed.

As described above, in some embodiments, the spectral properties of oneor more spectral fragments obtained from one or more pure componentspectra are used in the synthesis of the Zyoton and/or carrier kernel.In general, a spectral fragment is the portion of a spectrum between twowavelengths within the total wavelength range of the spectrum. Thewavelength boundaries of these spectral fragments may correspond to thewavelength boundaries of one or more features to be conditioned usingthe carrier kernel. In some embodiments, the spectral properties (e.g.,bandwidth, frequency distribution, etc.) of the spectral fragments areobtained at step 20 by applying a Fourier transform to a spectralfragment of the pure component spectra of the analyte of interest and/orone or more confounders typically present in the medium to be analyzed.Examples of analytes and confounders include glucose, urea, fat,collagen, water, if the medium to be analyzed is tissue or blood; gasessuch as radon, helium, etc., if the medium or environment to be analyzedis the atmosphere of the earth, another planet, etc.; or a chemical, ifthe medium to be analyzed is water in a reservoir, ocean, etc.

In step 22, one or more carrier kernels are synthesized using thespectral properties obtained in step 20 and/or additional propertiessuch as the expected required SCR increase, and/or the SNR of the systemto be used for data acquisition and measurement. In some embodiments,these various properties are used to synthesize a carrier kerneldirectly, while in some embodiments, these properties are used to designa Zyoton. A Zyoton may be obtained from a database 50, and theproperties thereof (e.g., the frequency distribution, amplitude profile,and numbers of k, m, and j components) may be determined at step 55. Asdescribed above, a carrier kernel may then be synthesized according tothe properties of the Zyoton such that the carrier kernel and the Zyotonare co-dependent.

Based on the selection of a Zyoton to be used in collision, aco-dependent carrier kernel is selected, e.g., in terms of the frequencycomponents and amplitude profile thereof, in step 24. The selectedcarrier kernel is modulated in step 30 using the feature, which may beprecursor modulated and/or interpolated, to obtain a conditionedfeature. The conditioned feature may be resampled at step 40 to matchits length with that of the Zyoton. The resampling may result in removalof one or more frequency components that were not included in thecarrier kernel and/or the Zyoton, but were introduced by the modulationin step 30. The modulation in the step 30 may be performed in the timedomain or in the frequency domain.

The conditioned feature may then be adjusted to ensure co-dependencythereof with the Zyoton. If the adjustment is performed in the timedomain, the time-domain amplitudes of the envelope peaks of theconditioned feature are adjusted such that the absolute differencebetween the velocity of the conditioned feature and the scaled velocityof the Zyoton is not greater than a kappa parameter κ_(DV2). If theadjustment is performed in the frequency domain, the frequency domainamplitudes of the k, m, and j components of the conditioned feature areadjusted such that the absolute difference between the spectral energyof the analyte-information representing k components of the conditionedfeature and scaled spectral energy of the k components of the Zyoton isnot greater than a frequency-domain value of kappa parameter κ_(DV2).Alternatively or in addition, the velocity/spectral energy of theconditioned feature may be scaled and, accordingly, a suitable kappaparameter can be used to adjust the conditioned feature. The numericscaling coefficient that establishes the spectral energy of the Zyotonwith respect to the spectral energy of the conditioned feature, isdenoted α_(Z).

In one embodiment for non-invasive glucose measurement, the variousparameters described above were selected such that: (i) the spectralenergy of the conditioned feature was adjusted to match 1/100,000^(th)the spectral energy of the Zyoton with which the conditioned feature wasto be collided. (ii) the conditioned feature waveform was propagated ona 10,000 point grid, and (iii) in this embodiment, precursor modulationusing a modulation signal at a frequency of 16.5 Hz was used in step 10.

The optional precursor modulation in step 10 is different frommodulation of the carrier kernel in step 30. In systems having lowinstrument resolution, low SNR, and/or low SCR, (i) the number of kfrequency components selected is typically greater than six, in order tocreate a collision computing system that may achieve the desiredaccuracy, and (ii) the frequency of the signal used for the optionalprecursor modulation in step 10 is also generally greater than 16.5 Hz,generally to bring the frequency components of the feature to a rangecomparable to those of the Zyoton and the carrier kernel. For example,the modulating frequency used for a system where the SNR is reduced byan order of magnitude and resolution reduced by a factor of two is 100KHz.

In various embodiments, the collision grid is not related to thewavelength or wavenumber scale associated with the acquired data fromwhich the features are generated. Instead, it is typically related tothe maximum of the cardinality of the total set of Zyoton frequencycomponents used in collision computing. The extracted feature can betreated as a one-dimensional data object including a vector of numbers.Once conditioned, the feature can represent an object on a spatial grid.The collision process is generally implemented on a spatio-temporalcollision grid having a time dimension and at least on spatialdimension, such as x, y, or z dimension, that captures waveformpropagation over time and a distance. The spatio-temporal collision gridcan thus represent traveling waveforms, i.e., the Zyoton, theconditioned feature, and the modified and renormalized Zyotons. Thenumber of spatial dimensions of the collision grid is equal to thenumber of spatial dimensions of the waveforms used in the collisions.Thus, if the waveforms are planar, the collision grid has two spatialdimensions. If the waveforms have three spatial dimensions, thecollision grid also has three spatial dimensions and the time dimension.The conditioned feature, the Zyoton, the modified Zyoton, and therenormalized Zyoton, are all travelling waveforms on the spatio-temporalcollision grid. A single collision iteration may analyzed over e.g., a1,000; 2,000, 5,000; 10,000; 20,000; 100,000 point collision grid.

The carrier kernel and the Zyoton properties are related and the two areco-dependent, because, among other reasons as described above, they bothdepend on the expected required SCR increase and/or the SNR of themeasurement system. Thus, both waveforms are dependent on the expectedSCR increase required to discern energy loss due to absorption at thefeature level. For some media/environments to be analyzed, the expectedrequired SCR increase can range from four to six orders of magnitudeusing Zyoton frequency bandwidths of hundreds of kHz to tens of MHz. Insome embodiments, the carrier kernel may optionally be frequency matchedto the Zyoton or may have a higher frequency bandwidth.

As described above, a conditioning process is applied to all of thefeatures of the acquired spectra, which generally involves frequencymodulation of a carrier kernel. Unlike a constant-frequency carriersignal typically used in typical amplitude modulation (AM) or frequencymodulation (FM), as in modulation of radio-frequency (RF) signals, thecarrier kernel modulated by the feature is a complex waveform itself,having several frequency components having different amplitudes. Acarrier kernel has three specific properties: (i) it is frequencymatched, at least to some degree, to the Zyoton; (ii) the Zyoton isdesigned so that its properties are unchanged within limits specified bydispersion velocity and divergence parameters when collided with theconditioned feature, in terms of morphology and peak frequencycomponents. As the preservation of Zyoton properties is a key designconstraint, the carrier kernel modulated by each feature is selectedsuch that Zyoton propagation after collision is not significantlyaltered, as specified by the dispersion velocity and divergenceparameters; and (iii) the carrier kernel is constructed to mitigateinterference from random noise, sampling variability, and othermeasurement transients in the feature and to improves the dynamic rangeof measurements.

Modulation of a carrier kernel generally provides smoothing of randomnoise in the feature and can increase dynamic range of measurement atthe same time. An example of a waveform family used to generate acarrier kernels, denoted G(t), is:

$\begin{matrix}{{G(t)} = {\frac{1}{2{\pi\mathbb{i}}}{\int_{{- i}\;\infty}^{i\;\infty}\left\lbrack {{{E(s)}^{- 1}{\mathbb{e}}^{st}\ {\mathbb{d}{s\left( {{- \infty} < t < \infty} \right)}}},{{{where}{E(s)}} = {\prod\limits_{1}^{\infty}\;{\left( {1 - \frac{s}{a_{k}}} \right){\mathbb{e}}^{s/b_{k}}}}},} \right.}}} & (12)\end{matrix}$and a_(k)=b_(k)+ic_(k) (k=1, 2, . . . ) being a sequence of complexnumbers such thatΣ_(k=1) ^(∞()1/b _(k))²<∞, andΣ_(k=1) ^(∞() c _(k) /b _(k))²<∞.The constant k in the above equation (which is different from the numberof analyte-information representing components k in a carrier kerneland/or a Zyoton), is set to 2000 in some embodiments so that theconditioning process can eliminate sampling-related transients that mayoccur.

A conditioned feature denoted as a Feature Waveform (FWi) in thecollision equation below, i.e., a carrier kernel modulated using afeature, must optionally match the time-domain length of its pairedZyoton (Zi). But the two, the Zyoton waveform and the conditionedfeature waveform, have typically different lengths in the time domain.To match the morphology, including the waveform lengths, a conditionedfeature may be down-sampled as described above in step 40 (FIG. 37),e.g., from 10,000 points to 2,000 points. Additionally, or in thealternative, the Zyoton can be down-sampled to match the lengths of thetwo waveforms. In some embodiments, the conditioned feature and/or theZyoton are up-sampled so that the lengths of their time-domainrepresentations match. Optional truncation of FWi is implemented toprune the collision spatio-temporal grid, e.g., for computationalefficacy. The choice of collision grid parameters is related to theselected properties of the Zyoton. For example, the length of thecollision grid must be greater than the length of a time-domainrepresentation of the Zyoton.

As described above, the co-dependency condition requires the change inpost-collision dispersion velocity to be less than a threshold κ_(DV1).The collision grid can establish a reference scale for the variableκ_(DV1). In general, the parameter κ_(DV1) is inversely proportional toboth the time and space dimensions of the collision grid. This has thegeneral effect of numerically establishing κ_(DV1) as a target value foreach system.

Amplitude adjustment of the conditioned feature is typically performedas described above, generally to adjust the amplitudes of the frequencycomponents of the conditioned features FWi to a fraction of the peakamplitudes of all Zyotons that may be used in the collision. Amplitudeadjustment completes the feature conditioning process, and isimplemented for all features e.g., those extracted from all acquiredspectra in a multiple illumination sequence (MIS), as described below.

The collision operation generally entails six steps. The first step isinitialization of the collision time scale. The next step is computationof the collision-computing parameters. The generalization of thecollision operator is given by equation (13):

$\begin{matrix}{{\Omega\left( {{\overset{\_}{FW}}_{i},{\overset{\_}{Z}}_{i}} \right)}_{t_{k}} = {\left\{ \begin{matrix}{ɛ\left( {\eta\left( {{\varpi\left( {{\overset{\_}{Z}}_{i},\overset{\_}{\alpha},\overset{\_}{\delta},\phi} \right)} \otimes {\rho\left( {{\overset{\_}{FW}}_{i},\overset{\_}{\beta},\overset{\_}{\delta}} \right)}} \right)} \right)} \\{ɛ\left( {\eta\left( {{\varpi\left( {{\overset{\_}{Z}}_{i},\overset{\_}{\alpha},\overset{\_}{\delta},\phi} \right)} \otimes {\rho\left( {\Omega\left( {,\overset{˘}{\beta},\overset{\_}{\delta}} \right)} \right)}} \right)} \right.}\end{matrix} \right.\begin{matrix}{k = 1} \\{k > 1}\end{matrix}}} & (13)\end{matrix}$where Ω(FW _(i), Z_(l) )_(t) ₁ is the result of a collision interactionbetween the feature wavefront FWi and Zyoton Z_(l) after the firstcollision. Also, Ω(FW _(i), Z_(l) )_(t) _(k) is the result of collisioninteraction between the renormalized feature wavefront resulting fromthe (k−1)th collision and Zyoton Zi.

The term k denotes collision iteration count in the above equation, andcovers the case that includes only a single collision, as well asmultiple (or

=k>1) collisions, where

is the total number of collision iterations, and is acollision-computing parameter.

Variable t_(k) ranging from 1 to k denotes the index on the grid forcollision, with t_(k), representing the kth point on the grid. ktypically ranges from 1 to 100,000 depending on the signal-to-clutterincrease desired.

are the renormalized results of (k−1)th collision that is used in thekth collision. The collision iterations can be performed in the timedomain or in the frequency domain.

In the time domain, the collision-computing parameter α denotes thescaling vector. The scaling depends on the desired dynamic range in thepost-collision energy change desired. In one embodiment, the scalingvectors are chosen to amplify the change in detected energy over adynamic range that extends over eight orders of magnitude. Such adynamic range can be required, e.g., if the original feature wereextracted from a spectrum acquired from a human subject with tissueglucose concentrations varying between 20 mg/dl and 600 mg/dl. In themathematics of Zyoton wavefront propagation dynamics, the scaling vectorrelates to the speed at which the zyoton wavefront propagates in media,some of which may be anisotropic or time-varying. In physical terms, thescaling vector α, can control the speed of the Zyoton wavefrontpropagation, and thus controls the amplification applied to the spectralenergy of the conditioned feature during the collision operation. Valuesof elements of α typically range between 10⁵ and 10⁻⁵, depending on theamplitude of the Zyoton waveform peaks in the time domain.

The collision-computing parameters of delay and phase rotation canmitigate noise. Some portion of the noise may be correlated with theoverall measurement system, e.g., the radiation emission and detectionsubsystem. Some portion of the noise, e.g., noise resulting fromproperties of the medium to be analyzed, may be uncorrelated to theoverall measurement system. δ denotes the delay shift vector used toalign the elements of the Zyoton and the conditioned feature wavefronts.The delay δ and phase rotations φ may be optionally applied to thetime-domain representation of the Zyoton or conditioned feature. Zyotonmorphology is related to the delay shift parameter, in that specificzyotons may have substantial numbers of closely-related frequencycomponents that require an appropriate selections of δ. This delay isrelated, in the glucose example, to the actual spectral wavelengthresolution of the instrument used to acquire the spectrum from which thefeature is extracted, with lower resolutions requiring larger delayvalues. This same δ may be used if all features have the samecardinality in terms of the number of spectral elements, e.g., 32 pointsin the noninvasive glucose embodiment. If the cardinality or featurelength is different, then a different δ is used for each feature. Thisdelay can also capture the expansion of the frequency bandwidth in theoriginal feature by the optional precursor modulation by theconditioning operation. Physically, δ compensates for the delay intransferring energy from principal frequency components of the originalfeature and those of the Zyoton. The numerical elements of the deltavector are related functions of the length of the Zyoton waveform in thetime domain, and to the amount of sensor noise. If a delay is notdesired, all values of δ are set to null. Proper δ selections allowprecise time-scale alignment of the feature waveform and Zyoton in thecomputer memory prior to collision.

Collision-computing parameter φ represents the phase rotation applied tothe Zyoton in the time domain, with values below π radians and typicallyranging between 0.1 radian and 0.0001 radian. If no phase rotation is tobe applied, then φ is set to 2 π radians. In addition to compensatingfor the dimensional deficiency of the zyoton described above, phaserotation is used to eliminate the impact of spectrum-to-spectrumvariations of random noise in the data, changes in scattering whichcould be due to changes in the medium, and changes in the absorption ofconfounders whose absorption overlaps with that of the analyte in thespectral region as of the feature.

Optionally, β and {hacek over (β)} are used to insure that the kappatest is met in the time domain. Collision-computing parameter denotes βthe optional scaling vectors for the conditioned feature wavefront, andcan be used if the Zyoton is not scaled in performing the Kappa test. Ifscaling is not desired, all values of β are set to unity. The β scalinggenerally impacts the amplitude of the time-domain peaks of theconditioned feature waveform, and can adjust the velocity of theconditioned feature waveform. Implicitly, this results in the scaling ofthe frequency domain amplitudes of the conditioned feature, leading toan adjustment of the energy of the conditioned feature waveform.

Collision-computing parameter {hacek over (β)} denotes the optionalscaling vectors for the renormalization of the modified Zyoton followingthe collision. If scaling is not desired, all the values of {hacek over(β)} are set to unity. This {hacek over (β)} scaling of amplitudes ofthe modified Zyoton is used to adjust its velocity in the time domain,and results in the scaling of frequency domain amplitudes of therenormalized modified Zyoton, and thereby and adjusts the energy of theZyoton. In various embodiments, this scaling is done so that kappatests, e.g. κ_(DV1) and/or κ_(DV3) tests, are met in the next collisioniteration. The scaling vectors β and {hacek over (β)} are notnecessarily related; the former is used in testing the velocitycondition of the two co-dependency conditions, and the latter is used toadjust the velocity during renormalization.

The parameter ω represents the fully conditioned Zyoton vector prior toa collision, wherein the conditioning operation includes of scalingusing α, and delay-shift δ and phase rotation φ operations. Theparameters α, δ and φ are interrelated and chosen such that the spectralenergy change during a collision between, for example, a feature withstrong analyte signal and one with weak analyte signal content derivedfrom the same spectrum could be separated by six to eight orders ofmagnitude. Calibration set data, using known concentrations of theanalyte of interest in a calibration medium, can be used to derive theseparameters. Improper or inconsistent selection will yield limitedutility in detection of analytes in the presence of confounders andbiological or instrument noise. If no scaling, delay shift or phaserotation is applied, then ω is set to unity. Typically ω is set to unityfor in-vitro analysis embodiments where the medium is much simpler thanin the tissue glucose embodiment.

The parameter ρ represents the fully conditioned feature-derivedwavefront FWi vector prior to a collision, wherein the conditioningoperation includes optional scaling using β, and delay-shift δoperations. The coefficients β and shift δ are selected in the similarmanner as for the Zyoton Wavefront. The collision operator, Zyotondesign and selection, feature conditioning and collision operatorparameters are codependent. The parameters β and δ are interrelated andchosen such that the spectral energy change during a collision betweenfor example, a feature with a strong analyte signal and one with a weakanalyte signal content derived from the same spectrum can be separatedby six to eight orders of magnitude during a collision. Calibration setdata, using known concentrations of the analyte of interest incalibration media are used to derive these parameters. If no scaling ordelay shift is applied, then ρ is set to unity.

As discussed herein, scaling takes two forms in the collision process.Prior to the first collision, the spectral energy of a Zyoton waveformis initially designed set to a multiple of the spectral energy of anexpected conditioned feature. After a collision, the modified Zyoton isrenormalized, which entails down-scaling in the frequency domain. Thedesign of the carrier kernel and zyotons is an iterative process, andthe initial waveforms chosen are refined as indicated by performance ofthe collision-computing process. The scaling vectors need to be computedprior to and after each collision, and are feature dependent.

The collision-computing parameter η denotes the bracket operator towhich the delay-shift δ is applied during collision. It represents thelocalization parameter for the collision. Different bracket lengths,e.g., of 100, 1000, or 2000 may be used. For example, a bracket lengthof 2000 frequency components is used for non-invasive measurement of theconcentration of some analytes. If no bracket operator is applied then,η is set to unity and the collision reduces to a phase rotation with ashift delay operation.

The collision-computing parameter ε denotes the compression operatorapplied to the collision process. This is used to squeeze the result(i.e., down-sample) the results of the wavefront to a fixed lengthpost-collision. If no compression is applied, then ε is set to unity.The generalized collision operator Ω(FWi, Zi) achieves a localizedexcitation of the Zyoton wavefront, propagating in a system withconstant velocity and colliding with a feature-derived wavefront suchthat the feature-wavefront presents a modulating influence on the stableZyoton. The energy transfer, i.e., loss during the collision, is relatedto the energy of the feature wavefront.

The collision grid is established prior to the collision. Optionalscaling of the Zyoton by α is also performed prior to the firstcollision. Any optional scaling of the conditioned feature waveform by βis also conducted prior to collision. Alignment of the frequencycomponents, achieved via delay and phase shift operations, is performedduring collisions. The alignment could optionally be performed before orafter the collisions in the frequency domain as well. Thecollision-computing parameters, including phase shift, delay, bracket,compression are used during the collision process.

Bracketing in the time domain can be achieved by truncating thetime-domain representations of a Zyoton waveform, a conditioned feature,and/or a renormalized Zyoton according to the time-domain length of thebracket. However, bracketing in the frequency domain is preferred.Alternatively or in addition, bracketing in the time domain can restrictthe zyoton dimensionality and/or or phase. The selected points of atime-domain waveform generally result in a corresponding bracket in thefrequency domain. As such, in various embodiments, bracketing isimplemented in the frequency domain by selecting a subset of fixednumber of frequency components k, m, and j of the conditioned feature.The frequency domain bracket length specifies the total number offrequency components of a waveform that are selected. In variousembodiments, the k components are not removed during the truncation thatis performed during the implementation of a bracket. A key differencebetween truncation as part of renormalization and frequency domainbracketing is that in renormalization the energy of the removedcomponents is redistributed, while in bracketing such redistribution isnot done because frequency components (typically the j components) fromthe Zyoton and the conditioned feature or renormalized Zyoton areremoved.

During the overall collision process, the truncation operation isoptionally performed at three steps: In step (i) during the featureconditioning process when convolving the feature with the carrier kernelfor the purpose of making a conditioned feature and the Zyoton the samelength in the time domain, and optionally for computational efficacy astruncation reduces the size of the collision grid; in step (ii) duringthe collision operation, through the bracketing operation in thefrequency domain to constrain the set of resulting frequency componentsto capture energy changes in the spectral feature due to absorption bythe analyte and to delete frequency components that are only related torandom scattering losses; and in step (iii) during the renormalizationstep, in the frequency domain, to remove frequency components that notare not related to energy absorption by the analyte.

In some embodiments, the collision process may be implemented in thefrequency domain, where the symbol

represents a bracketed interaction operator which effects the collisionprocess described below. The bracketed interaction typically involvesfrom one to several thousand frequency components of the Zyoton and theconditioned-feature waveforms. For computational efficacy, efficient useof storage, and to immunize the system against random noise, typicallyonly selected frequency components are used in the post-collision energychange computations. The bracketed interactions are set such that allfrequency components in the conditioned feature waveform and originalZyoton that contribute to the computation of energy gain are used.

More importantly, the truncation window (or the number of frequencycomponents retained after collision) is typically chosen to be longenough to accommodate all the frequency components of original waveformsthat are likely to contribute to the computation of the energy gain dueto the analyte over the complete set of collisions in each collisioniteration and over all collision iterations. For example, in oneembodiment where the energy computation uses 6 to 20 k-frequencycomponents, but involves 20,000 collisions, the number of retainedfrequency components was chosen to be 1,000, after several trials, toamplify energy absorbed by the analyte while eliminating the absorptionof energy by confounders and the effects of scattering and random noise.

The table below describes different stages of the overall collisionprocess for different types of collisions. (All operations are assumedto occur in the frequency domain):

TABLE 8 Number of Number of Number of Number of Frequency FrequencyFrequency Frequency Components in Components in Components In Componentsin the Original the Conditioned the Modified the Renormalized Zyoton (Z)Feature (CF) Zyoton (Z′) Zyoton (Z″) At Synthesis, (k + m + j) = 10,000(k + m′ + j′) = 11,000 (Z′) does not exist (Z″) does not exist Prior toAny Collisions After the (k + m + j) = 2,000 (k + m + j) = 2,000 (Z′)does not exist (Z″) does not exist Bracketing Energy of the Energy ofthe Performed Prior 8,000 frequency 9,000 frequency to the Firstcomponents that components that Collision are removed is are removed isnot redistributed not redistributed across the across the remaining2,000 remaining 2,000 components components After the First With respectto CF does not exist (k + m″ + j″) = 2,200 (Z″) does not Collision thecompleted exist prior to collision renormalization iteration, Z does notexist. For the next collision iteration, previously bracketed Z can beextracted from memory (k + m + j) = 2,000 After the First Same as above.CF does not exist (Z′) does not exist (k + m + j) = 2,000Renormalization, (k + m + j) = 2,000 after renormalization Energy of theWhich Is Same 200 frequency As Prior to the components Next Collisionthat are Iteration removed is redistributed across the surviving (m + j)components

Collision computing provides a mechanism whereby a source waveform iscollided, (through the pseudo-convolution process described above in acomputer processor) with a Zyoton, a waveform constructed to function asan energy amplification mechanism. The medium properties may be constantor time-varying (due to diffusion, flow, etc.). Also, the medium may beisotropic or anisotropic, and of uniform composition or spatiallyvarying composition.

Process of Collision Computing

As described earlier, a Zyoton is a traveling waveform, i.e., a Zyotonhas a temporal dimension and at least one spatial dimension. Arepresentative Zyoton Z includes k high energy components havingamplitudes and frequencies as: (A₁, Ω_(Z1)), (A₂, Ω_(Z2)), . . . ,(A_(k), Ω_(Zk)), where k>0; optionally, m medium energy componentshaving amplitudes and frequencies as: (A_(k+1), Ω_(Zk+1)), (A_(k+2),Ω_(Zk+2)), . . . , (A_(k+m), Ω_(Zk+m)), if m>0; and j low energycomponents having amplitudes and frequencies (A_(k+m+1), Ω_(Zk+m+1)),(A_(k+m+2), Ω_(Zk+m+2)), . . . , (A_(k+m+j), Ω_(Zk+m+j)), where j>0. Arepresentative conditioned feature CF that is to be collided with therepresentative Zyoton Z, where CF is also a traveling waveform,generally has at least k+m′+j′ frequency components: (a₁, Ω_(CF1)), (a₂,Ω_(CF2)), . . . , (a_(k), Ω_(CFk)), (a_(k+1), Ω_(CFk+1)), (a_(k+2),Ω_(CFk+2)), . . . , (a_(k+m′), Ω_(CFk+m′)), (a_(k+m′+1), Ω_(CFk+m′+1)),(a_(k+m′+2), Ω_(CFk+m′+2)), . . . , (a_(k+m′+j′), Ω_(CFk+m′+j′)), wherem′+j′≧m+j.

FIG. 17 illustrates the collision between a representative zyoton Z anda representative conditioned feature CF on a synthetic “collisionspace-time” domain grid. FIG. 18 symbolically depicts thesynthetic-domain collision, where the wavefronts of Z and CF collide ata synthetic line of collision on the synthetic space-time grid at timet₀. In the real time domain, the velocity of a Zyoton is several times(e.g., a few hundred, a few thousand, a few hundred thousand times,etc.) greater than the velocity of the conditioned feature. Therefore,in the real time-domain collision, the conditioned feature is virtuallystationary relative to the Zyoton, and during collision, the Zyotonsweeps across the conditioned feature.

In various embodiments, the Zyoton-conditioned feature collision iscomputationally implemented in the frequency domain. To this end, amagnitude spectrum of the frequency components of a Zyoton can beobtained by applying a Fourier transform to a time-domain Zyotonwaveform, and, similarly, a magnitude spectrum of the frequencycomponents of a conditioned feature can obtained by applying a Fouriertransform to a time-domain conditioned feature waveform. Zyotonssynthesized from generator functions, polynomial sequences, or one ormore waveform families enumerated above, are first generated asnumerical sequences, where the elements of the numerical sequence areconsidered to be analogous to a time domain representation of theZyoton.

In various embodiments, the frequency-domain collision of Z and CF isimplemented using the respective sorted magnitude spectra thereof, i.e.,magnitude spectra sorted by amplitudes. In a frequency-domain collision,the frequency components of the Zyoton interact (“collide”) withselected components of the conditioned feature in a carefully controlledprocess called bracketed collision interaction. A pictorialrepresentation of the collision process is shown in FIG. 57 in asynthetic grid, i.e., regardless of the domain of implementation, wherethe components of the zyoton Z are shown as moving from left to right,and the components of the conditioned feature, CF move from right toleft toward a line of collision or interaction at the center.

Each successive row, moving from top to bottom, represents one “timeunit” of this synthetic grid, i.e., the in the top row, the twocomponents Z1 and CF1 have not yet interacted; on the second row Z1 andCF one have interacted, indicated by “Z1 CF1” in the center. The “Z1CF1” designation and similar designations “ZiCFi” in the subsequent rowsin FIG. 57 does not imply a conventional convolution or a simplemultiplication of the two elements. Rather this designation symbolicallyrepresents the collision interaction between elements Zi and CFi. Inactuality, the collision interaction with each Zi involves more than oneconditioned feature components, as controlled by the collision bracketlength, as described below, but in the symbolic representation only CFiis shown for clarity. At the right of the second row is shown a newfrequency component, Z′1, of the modified Zyoton. Here again, inactuality as described below, a number of new modified Zyoton componentsmay be produced in each collision interaction, but only one is shown inthis symbolic representation for clarity.

Each pair of components interacts successively as described below,producing new frequency components of the modified zyoton, Z′2, Z′3,etc., from the interaction. These new components include the energytransferred from the conditioned feature to the modified Zyoton duringthe collision process. FIGS. 46B-47C depict a sorted (in descendingorder) magnitude spectrum of a Zyoton. The Y axis shows the amplitudesand the X axis shows frequencies according to an index and not actualfrequencies because in a sorted magnitude spectrum, the frequencies aretypically not in a sorted order.

In the representations of Zyotons and conditioned-feature describedabove, without the loss of generality:

A₁>A₂> . . . >A_(k)>A_(k+1)>A_(k+2)> . . . >A_(k+m)>A_(k+m+1)>A_(k+m+2)>. . . >A_(k+m+j); and a₁>a₂> . . . >a_(k)>a_(k+1)>a_(k+2)> . . .>a_(k+m′)>a_(k+m′+1)>a_(k+m′+2)> . . . >a_(k+m′+j′).

In general, for a component index v, amplitude A_(v)>A_(v+1) andamplitude a_(v)>a_(v+1), but Ω_(Zv) can be greater than or less thanΩ_(Zv+1) and, similarly, Ω_(CFv) can be greater than or less thanΩ_(CFv+1).

The Zyoton and the conditioned feature to be collided therewith areconstructed, however, such that for each of the k components: |Ω_(Zv)_(k) −Ω_(CFv) _(k) |≦ε_(k)Ω_(Zv) _(k) , v^(k)=1, . . . , k. In variousembodiments, ε_(k) can range from 0.0001 up to 0.0005. Thus, ifε_(k)=0.005, for each k component, having a component index v^(k), thefrequency of the conditioned feature, denoted Ω_(CFv) _(k) , is within(i.e., neither greater than nor less than) 0.05% of the frequency of theZyoton, denoted Ω_(Zv) _(k) . Furthermore, for each of the m components:|Ω_(Zv) _(m) −Ω_(CFv) _(m) |<ε_(m)Ω_(Zv) _(m) , v^(m)=(k+1), . . . ,(k+m), and for each of the j components: |Ω_(Zv) _(j) −Ω_(CFv) _(j)|<ε_(j)Ω_(Zv) _(j) , v^(j)=(k+m+1), . . . , (k+m+j). Collectively, wedefine the constraint imposed by ε_(k), ε_(m) and ε_(j) as EpsilonTests. In various embodiments, ε_(m) can range from 0.001 up to 0.025,and ε_(j) can range from 0.001 up to 0.1. Thus, if ε_(m)=0.025, for eachm component, having a component index v^(m), the frequency of theconditioned feature, denoted Ω_(CFv) _(m) , is within 2.5% of thefrequency of the Zyoton, denoted, Ω_(Zv) _(m) . Similarly, if ε_(j)=0.1,for each j component, having a component index v^(m), the frequency ofthe conditioned feature, denoted, Ω_(CFv) _(j) , is within 10% of thefrequency of the Zyoton, denoted Ω_(Zv) _(j) .

In some situations, a conditioned feature CF may have extra m and/or jcomponents. In one example, the Z has six k components (Z1-Z6), three mcomponents (Z7-Z9), and five j components (Z10-Z14). The CF to becollided with Z has six k components (indexed CF1-CF6), but four mcomponents (CF7-CF10), and six j components (indexed CF11-CF16). In suchcases the frequency relationship |Ω_(Zv) _(m) −Ω_(CFv) _(m)|<ε_(m)Ω_(Zv) _(m) and |Ω_(Zv) _(j) −Ω_(CFv) _(j) |<ε_(j)Ω_(Zv) _(j) isimposed as before for the corresponding Z and CF components identifiedby the indices v^(m) and v^(j). For some CF components, however, thereis no corresponding Z component. In the foregoing example, CF10, an mcomponent, does not correspond to Z10, which is a j component of theZyoton. The Epsilon Tests are nevertheless satisfied in variousembodiments for these unmatched components by ensuring that thefrequency of an unmatched CF component of the “m” group is within ε_(m)of at least one m component of Z. Similarly, it is ensured in variousembodiments that the frequency of an unmatched CF component in the “j”group is within ε_(j) of at least one j component of Z. For example,CF10 must be within ε_(m) of any one of Z7 through Z9, and each of CF15and CF16 must be within ε_(j) of any one of Z10 through Z14. If thiscondition is not met, the kappa test(s), described elsewhere, may failand a redesign of either the zyoton, the carrier kernel, or both, may berequired.

The conditioned feature is obtained via a frequency modulation of thecarrier kernel by the feature. The feature may have been optionallyfrequency modulated, using a pre-cursor modulation signal such as asinusoidal signal having a frequency of 16.5 Hz, 60 Hz, 100 Hz, 1.2 kHZ,100 kHz, 175 kHz, etc. Even if frequencies of all k (and m and/or j)components of the carrier kernel are initially selected to be identicalto the corresponding Zyoton component frequencies, this modulation cancreate slight differences between the frequencies of the k (and m and/orj) components of the conditioned feature and those of the unmodulatedcarrier kernel. The amplitude/magnitude sorted Zyoton and conditionedfeature, where the frequencies of the respective Zyoton and conditionedfeature components are related according to ε_(k), ε_(m), ε_(j), aredenoted F(Z) and F(CF), respectively.

The frequency-domain collisions are implemented on a frequency domaincollision grid, with collision coefficients including a collision gridlength K≦(k+m+j) and a bracket length CB <(k+m+j). If the collisionbegins at the interaction step g₀ on the collision grid, at step g_((i))the frequency component F_(Z(i))) of the Zyoton F(Z) interacts with acorresponding frequency component F_(CF(i)) of the conditioned featureF(CF). Note that these interaction steps do not necessarily correspondto the real time associated with the traveling waveforms in the timedomain. In a computer implementation, the time period between successivegrid points, i.e., computation steps can be set to the reciprocal of thelength of the Zyoton frequency vector used in the collision times thesquare of the length of the collision bracket,

${i.e.},{{{time}\mspace{14mu}{period}} = {\frac{1}{\left( {k + m + j} \right)*{CB}^{2}}.}}$“Time” here is the duration of computation/interaction steps involved ina collisions that includes all interactions between Zyoton andconditioned feature frequency components during a single iteration ofthe overall collision process. A single collision iteration can producea maximum of (K−δ)*CB frequency components of the modified Zyoton, whereδ represents a shift-delay. If no shift-delays are needed, δ is equal tozero. The frequency-domain collision grid can therefore be representedas a numerical vector of time points or indices {g₀, g₁ . . .g_((K−δ)*CB)}. This number of interaction steps in a single collisioniteration is different from the number of steps required in anelement-by-element multiplication, and in a conventional convolution, aswell, for the reasons described below.

The collision interactions can be carried out in configurations rangingfrom completely parallel implementation, where each Zyoton frequencycomponent interacts simultaneously with each conditioned featurefrequency component from the corresponding bracketed set of CF frequencycomponents, to a completely sequential implementation, where eachoperation in each interaction occurs one at a time, in sequence. Invarious embodiments, the number of grid points of the collision grid inthe frequency domain can vary depending on the computationalconfiguration employed, but more grid points are generally required asthe configuration becomes more sequential.

The collision-computing coefficient, δ≧0, is an index shift parameter(i.e., it shifts frequency components of the Zyoton) or a delaycoefficient in frequency domain collisions. If δ takes values greaterthan 0, it can result in shifts of the Zyoton frequency components thatinteract with the frequency components of the conditioned feature.

With reference to FIGS. 38-41, in one example, N=k+m+j=10 and CB=4, andδ=0, and, as such, collisions can be performed for the Zyoton componentsZ1 through Z7. The collision grid length K=N−CB+1 is 7, for a partiallysequential, partially parallel implementation. The minimum number ofinteraction steps, however, is (K)*CB where each frequency componentinteraction is performed in a sequential manner over all K Zyotoncomponents and associated K brackets of CF components; or K where eachCF component of the collision bracket interacts with the correspondingZyoton component in parallel. In this example, the shift coefficient δis zero. For computational efficacy, a collision grid can be set to beevenly spaced with a time interval of 1 picosecond, 1 nanosecond, 1microsecond, 1 millisecond, or 1 second, up to 1 minute. In someembodiments, the time interval is set to be less than

$\frac{1}{\left( {k + m + j} \right)*{CB}^{2}}$seconds.

The result of a collision interaction between the Zyoton Z and theconditioned feature CF according to various embodiments, when convertedback to the time domain, is a non-invertible combination of the Zyotonand the conditioned feature. In the frequency domain, this interactioncan be described as bracketed conditional amplitude multiplicationsbetween each Z and a set of CF components, and conditional summations ofthe amplitudes of two or more components resulting from the bracketedmultiplication. As described below, the conditions for the conditionalamplitude multiplication and for the conditional amplitude summationsare whether the frequencies of interacting components match.

For the conditional multiplication, the amplitudes of a pair of Z and CFcomponents are multiplied if and only if the frequencies of those twocomponents satisfy an applicable Epsilon test. The applicable Epsilonvalue (i.e., ε_(k), ε_(m), or ε_(j)) is determined according to theenergy group (i.e., k, m, or j) to which the Z component of theinteraction belongs. Similarly, for a conditional summation theamplitudes of two or more resulting components of the overall collisioninteraction are summed if and only if the frequencies thereof satisfythe Epsilon test applied to the Zyoton component with the largestmagnitude. The conditional multiplications and summations generallymakes the collision interaction non-invertible. While conventionalmodulations techniques are generally invertible, the overall collisionprocess described herein, which may additionally include scaling,shifting, and/or phase rotation of frequency components, is not aconventional modulation, and is generally not invertible.

Post-collision, the modified Zyoton generally includes new frequencycomponents that were not present in the original Zyoton and theconditioned feature. Interactions between the Zyoton and the conditionedfeature described below may introduce new frequency components, butbecause of the amplitude mismatch between the frequency components ofthe Zyoton and those of the conditioned feature, the amplitudes of thosenew frequency components are typically smaller than the amplitudes ofthe k components of the Zyoton. The renormalization process is designedto remove some of these components via truncation.

The frequency-domain collision of the Zyoton and the conditioned featuremay then be expressed in the form of a pair-wise (i.e., component bycomponent) conditional multiplication of the (optionally shifted,scaled, and/or phase-rotated) components of the zyoton by all thecomponents of the conditioned feature within a bracket. This can beexpressed as:F′(Z′)=LI ₁ ^(K)(LI _(t−δ) ^(t−δ+CB)(α ^(f)(φ^(F)(Z _((g) _((t−δ) _(f) ₎₎))

CF _((g) _((t)) ₎)),t=0,1, . . . ,(k+l+m)−CB  (14)where F′ (Z′) is the unsorted magnitude spectrum of modified Zyotonfrequency components produced by the collision, and may includeadditional frequency components. The operator LI₁ ^(CB)(..) representsthe set of conditional co-products that includes the product termsresulting from the interactions between a single Zyoton component Z_(g)with all the conditioned feature components CF_(g), CF_(g+1), . . . ,CF_((g+CB-1)) over the bracket length CB, and the operator LI₁ ^(K)(..)represents the conditional co-product over the interactions of all thecomponents of the Zyoton Z_(g1), Z_(g2), . . . , Z_(K), with all theconditioned feature components within the respective brackets [g₁,g_(1+CB-1)], [g₂, g_(2+CB-1)], . . . [g_(K), g_(K+CB-1)] that occurduring all the steps of a single collision. The term co-productgenerally refers to one or more multiplications and sums of theproducts. Unlike the conventional co-product, multiply-add, and/ormultiply-accumulate operations, however, these co-products areconditional, as described herein.

A bracketed conditional multiplication operator,

, of Z_(gp) and [CF_(gp), CF_(gp+1), . . . , CF_((gp+CB-1))] can yield[Z′_(gp), Z′_(gp+1), . . . , Z′_((gp+CB-1))] as follows:

Case (a) Zgp is a k component: By the construction of Z and CF, asdescribed above, the frequencies of the pair Ω_(Zgp) and Ω_(CFgp) mustsatisfy the ε_(k) test. Therefore, the frequency of the result of aninteraction between Z_(gp) and CF_(gp), which would produce the modifiedZyoton component Z′_(gp), is designated the frequency Ω_(Zgp); thus,Ω_(Z′gp)=Ω_(Zgp). The amplitude of Z′_(gp) is computed asA′_(gp)=A_(gp)×a_(gp).

For the remainder of the collision bracket, i.e., for each CF componentCF_(gp+l), where l=1 . . . CB-1, unless the frequencies Ω_(Zgp) andΩ_(CFgp−l) satisfy the ε_(k) test, no interaction between Z_(gp) andCF_(gp+l) occurs. If the ε_(k) test would succeed for a particular valueof 1, by construction, Ω_(Zgp−l) would be within ε_(k) times Ω_(Zgp). Inthis situation, the shift-delay operator, as described below, may beapplied and, interaction of the collision bracket may not occur witheither Z_(gp) and Z_(gp+l). Thus, in general, for the k components,Z_(gp) interacts only with CF_(gp) in the collision bracket and not withCF_(gp+l), l=1 . . . CB-1. Thus, no new k components are generated, ingeneral.

Case (b) Zgp is an m component: By the construction of Z and CF, asdescribed above, the frequencies of the pair Ω_(Zgp) and Ω_(CFgp) mustsatisfy the ε_(m) test. Therefore, Z_(gp) and CF_(gp) would interact,producing a modified Zyoton component Z′_(gp). The amplitude of Z′_(gp)is computed as A′_(gp)=A_(gp)×a_(gp). If the frequencies Ω_(Zgp) andΩ_(CFgp) satisfy the stricter ε_(k) test, the frequency of Z′_(gp) isdesignated the frequency Ω_(Zgp); thus, Ω_(Z′gp)=Ω_(Zgp). Otherwise, thefrequency designated to of Z′_(gp) is the sum of Ω_(Zgp) and Ω_(CFgp).

For the remainder of the collision bracket, i.e., for each CF componentCF_(gp+l), where l=1 . . . CB-1, unless the frequencies Ω_(Zgp) andΩ_(CFgp+l) satisfy the ε_(m) test, no interaction between Z_(gp) andCF_(gp+l) occurs. If the frequencies satisfy the ε_(m) test, a newmodified Zyoton component Z′_(gp+l) is generated, and the amplitudethereof is computed as A′_(gp)=A_(gp)×a_(gp). If Ω_(Zgp) and Ω_(CFgp−l)satisfy the ε_(k) test, the frequency of Z′_(gp+l), i.e., Ω_(Z′gp+l), isset to Ω_(Zgp); otherwise Ω_(Z′gp+l)=Ω_(Zgp)+Ω_(CFgp+l). If all CFcomponents in the collision bracket satisfy the ε_(m) test, CB−1 newmodified Zyoton components would be created. If no CF component in thecollision bracket satisfies the ε_(k) test, however, all of the newlycreated modified Zyoton components would be designated frequenciesaccording to Ω_(Z′gp+l)=Ω_(Zgp)+Ω_(CFgp+l). Unless all of thesefrequencies strictly match (i.e., they satisfy the ε_(k) test) withfrequencies of the original Zyoton and/or conditional feature, themodified Zyoton would have one or more new frequencies. Often, one ormore but not all of the CF components of the bracket may interact withΩ_(Zgp) and one or more new frequencies may be generated.

Case (c) Zgp is a j component: By the construction of Z and CF, asdescribed above, the frequencies of the pair Ω_(Zgp) and Ω_(CFgp) mustsatisfy the ε_(j) test. Therefore, Z_(gp) and CF_(gp) would interact,producing a modified Zyoton component Z′_(gp). The amplitude of Z′_(gp)is computed as A′_(gp)=A_(gp)×a_(gp). If the frequencies Ω_(Zgp) andΩ_(CFgp) satisfy the stricter ε_(k) test, the frequency of Z′_(gp) isdesignated the frequency Ω_(Zgp); thus, Ω_(Z′gp)=Ω_(Zgp). Otherwise, thefrequency designated to of Z′_(gp) is the sum of Ω_(Zgp) and Ω_(CFgp).

For the remainder of the collision bracket, i.e., for each CF componentCF_(gp+l), where l=1 . . . CB-1, unless the frequencies Ω_(Zgp) andΩ_(CFgp+l) satisfy the ε_(j) test, no interaction between Z_(gp) andCF_(gp+l) occurs. If the frequencies satisfy the ε_(j) test, a newmodified Zyoton component Z′_(gp+l) is generated, and the amplitudethereof is computed as A′_(gp)=A_(gp)×a_(gp). If Ω_(Zgp) and Ω_(CF+l)satisfy the stricter ε_(k) test, the frequency of Z′_(gp+l), i.e.,Ω_(Z′gp+l), is set to Ω_(Zgp); otherwise Ω_(Z′gp+l)=Ω_(Zgp)+Ω_(CFgp+l).If all CF components in the collision bracket satisfy the ε_(j) test,CB-1 new modified Zyoton components would be created. If no CF componentin the collision bracket satisfies the ε_(k) test, however, all of thenewly created modified Zyoton components would be designated frequenciesaccording to Ω_(Z′gp+l)=Ω_(Zgp)+Ω_(CFgp+l). Unless all of thesefrequencies strictly match (i.e., they satisfy the ε_(k) test) withfrequencies of the original Zyoton and/or conditional feature, themodified Zyoton would have one or more new frequencies. Often, one ormore but not all of the CF components of the bracket may interact withΩ_(Zgp) and one or more new frequencies may be generated.

After the bracketed interactions for all Zyoton components aregenerated, the components of the modified Zyoton are amplitude sorted,and designated as k, m, j components according to the amplitudesthereof. Thereafter, all of these components are compared in a pairwisemanner. For a component designated as a k component, if the frequency ofthat component matches with the frequency of any other component, i.e.,the frequencies satisfy the ε_(k) test, those two components are merged.To this end, the amplitudes of these two components are summed the sumis set as the amplitude of one of the components in the matching pair,and the other component is removed. In some embodiments, the componentthat is retained is designated the greater of the frequencies of thecomponents of the pair. In some embodiments, the lesser frequency may bedesignated to the retained component, while in some embodiments, thefrequency of the retained component is not changed.

In the pairwise comparisons, for a component designated as an mcomponent, the frequency comparison and conditional merging, i.e.,conditional sum of the amplitudes, is performed as described above,except the ε_(m) test is applied instead of the ε_(k) test. In thepairwise comparisons, for a component designated as an j component, thefrequency comparison and conditional merging, i.e., conditional sum ofthe amplitudes, is performed as described above for a k component,except the ε_(j) test is applied instead of the ε_(k) test. The retainedcomponents may be amplitude sorted, yielding a modified Zyoton.

To illustrate the collision interactions, with reference to FIGS.58A-58D, for the Zyoton component Z1 , the collision bracket includesthe CF components: {CF1, CF2, CF3, CF4}. With reference to FIG. 58B, theonly collision interaction that occurs for the component Z1 , however,is Z1 CF1, because CF1 is the only CF component in the bracket thatsatisfies the ε_(k) test. For the Zyoton component Z2, the collisionbracket includes the CF components {CF2, CF3, CF4, CF5}. Only the Z2CF2interaction occurs, because CF2 is the only component in Z2's bracketthat satisfies the ε_(k) test with respect to Z2. Similarly, for theZyoton component Z3, only the Z3CF3 interaction occurs. In each of theseinteractions, the amplitude of the resulting modified Zyoton components,denoted Z1 ′, Z2′, Z3′, respectively, are the respective products of theamplitudes of the corresponding Z and CF components. For example, theamplitude of Z1 ′ is the product of the amplitudes of Z1 and CF1. Thefrequency of Z1 ′ is set to be the frequency of Z1 because, bydefinition, the frequencies of Z1 and CF1 satisfy the ε_(k) test.

In FIG. 58B, this is illustrated by the computation of Z′1, Z′1_1,Z′1_2, and Z′1_3. As the bracket length is 4, the collision bracketcorresponding to Z1 includes four CF components, namely {CF1, CF2, CF3,and CF4}. By construction, the frequencies of Z1 and CF1 satisfy theε_(k) test and, as such, Z′1 is designated the frequency of Z1, 260 kHz.In some embodiments, the frequency of the Zyoton component is chosen asthe frequency of the modified Zyoton component, if a k component of theZyoton is involved in the collision interaction. Otherwise, if an m or jcomponent of the Zyoton is involved, the frequency of either the Zyotoncomponent or the conditioned feature component may be chosen as thefrequency of the resulting modified Zyoton component. The amplitude ofZ′1 is the product of the amplitudes of Z1 and CF1. Z1 conditionallycollides with the other CF components in the bracket, but thefrequencies of these CF components do not satisfy the ε_(k) test whencompared to the frequency of Z1 and, as such, the results of theseunperformed interactions are shown as shown as “--” entries. Theinteraction of Z1 and CF2 fails to meet the ε_(k) test and, hence, thecorresponding entry Z′1_1 is designated “--”; similarly, Z′1 _(—2) andZ′1_3 are also designated “--”. The frequency of Z′1 is the frequency ofZ1 , and no k components having new frequencies are created.

With reference to FIG. 58C, for the m component Z5, the collisionbracket includes the CF components {CF5, CF6, CF7, CF8}. The componentsZ5 and CF5 interact because their frequencies satisfy the ε_(m) test.There is no interaction between Z5 and the components CF6 and CF7,because the pairs (Z5, CF6) and (Z5, CF7) do not satisfy the ε_(m) test.The components Z5 and CF8 interact, however, because they satisfy theε_(k) test. Thus, the collision of Z5 with the CF components within Z5'scollision bracket produces two modified Zyoton components, namely, Z5′and Z5′_3. The amplitudes of these two modified Zyoton components aredetermined by the product of the amplitudes of Z5 and CF5 and theproduct of the amplitudes of Z5 and CF8, respectively.

The components Z5 and CF8 satisfy the stricter ε_(k) test and, as such,the frequency of Z5′ is set to be the frequency of Z5. While thecomponents Z5 and CF8 satisfy the ε_(m) test, they do not satisfy theε_(k) test and, as such, the frequency of Z5′_3 is set to be the sum ofthe frequencies of Z5 and CF8. As such, a modified Zyoton componenthaving a frequency different from the frequencies of any of the Zyotonand conditioned feature components is created. The amplitudes of thesenew components are most likely to be within the m region of the modifiedZyoton, but depending on the amplitudes of Z5,CF5, and CF8, one or bothof these amplitudes may be in the j region of the modified Zyoton. Ingeneral, because the m-component amplitudes are much lower than thek-component amplitudes, the new component magnitudes typically do notreach the magnitude region of the k components.

With reference to FIG. 58D, for the j component Z7, the collisionbracket includes the CF components {CF7, CF8, CF9, CF10}. Here again, byconstruction, the frequencies of Z7 and CF7 satisfy the ε_(j) test and,as such, an interaction between these two components is permitted. Thatinteraction produces the modified Zyoton component Z′7. The componentsCF8 and CF9 do not satisfy the ε_(k) test with respect to Z7 and, assuch, these two CF components do not interact with Z7. The componentCF10 satisfies the ε_(k) test, however, and interacts with Z7, producingthe modified Zyoton component Z′7_3.

As described above, the amplitude of Z′7 is the product of theamplitudes of Z7 and CF7, and the amplitude of Z′7_3 is the product ofthe amplitudes of Z7 and CF10. Neither CF7 nor CF10 satisfies thestricter Σ_(k) test and, as such, the frequency of Z′7 is set to be thesum of the frequencies of Z7 and CF7 (i.e., 510 kHz), and the frequencyof Z′7_3 is set to be the sum of the frequencies of Z7 and CF8 (i.e.,480 kHz). While 480 kHz is a new frequency, the frequency of Z′5 is 500kHz. Z′5 is likely an m component of the modified Zyoton, and thecomponents Z′5 and Z′7 satisfy the ε_(m) test. Therefore, these twocomponents can be merged. As Z′5 is the larger component by amplitude,the amplitude of Z′5 is reset as the sum of the initially computedamplitude of Z′5 (i.e., 1482) and the amplitude of Z′7 (i.e., 12.54).Thus, the new amplitude of Z′5 is set to be 1494.94. The mergedcomponent Z′7 is removed from the modified Zyoton. In this example, thefrequency of the retained component Z′5 is not modified, and remains tobe 500 kHz. In some embodiments, the larger of the frequencies of thetwo components may be designated to the retained components. In otherembodiments, the smaller frequency may be designated, and in someembodiments the frequency of the removed component may be designated tothe retained component.

In general, for each of K Zyoton components, up to CB modified Zyotoncomponents may be generated initially, as described above, for a totalof (K*CB) initial modified Zyoton components, where CB is the bracketlength. Frequencies of these components are checked pairwise todetermine pairs having matching frequencies, where the match can bedetermined according to the applicable Epsilon test. To determine theapplicable Epsilon test, for a pair of components of the modified Zyotonthat are under evaluation for a possible frequency match, the energyregion (i.e., the k, m, or j region) to which the component having thegreater amplitude likely belongs is determined. If the component likelybelongs of the k region, the ε_(k) test is applied. If the componentlikely belongs to the m region, ε_(m) test is applied. Otherwise, theε_(j) test is applied. The matching pairs are merged, similarly as Z′5and Z′7 are merged, by summing the respective amplitudes thereof. Two ormore initially generated modified Zyoton components may be conditionallymerged together. In various embodiments, the final components of themodified Zyoton, obtained after conditional merging, are sorted byamplitudes. The conditional merging typically removes one or moremodified Zyoton components. The renormalization process describe abovemay additionally remove one or more components of the modified Zyotonand may redistribute the energy of such additionally removed components.

As described above, these collision interactions, even during a singleiteration of the overall collision process, typically results in newmodified Zyoton frequency components having frequencies that are notpresent in the original Zyoton and/or the conditioned feature in the jand m regions.

In general, in the bracketed interaction, the Zyoton components areordered by amplitudes thereof and, as such, gp through gp+K−1 correspondto the component indices of Z. One or more new frequencies may beassociated with the modified Zyoton components identified by the indicesZ′_(gp1) through Z′_(gp) _(_) _((CB-1)), for all gp in the range from 1through K. All of these modified Zyoton components may be sequentiallyindexed from 1 through K+U, where U is the number of new components ofthe modified Zyoton in the m and j regions. All of the K+U components ofthe modified Zyoton are not necessarily amplitude-sorted after thecollision interactions. As such, the collision of Z and CF producesmodified Zyoton components that are not necessarily magnitude sorted. Insome embodiments, prior to renormalization, these components are sortedaccording to the amplitudes thereof. The frequencies of the k componentsof the Zyoton Z are preserved during the generation of the modifiedZyoton, as described above, and these k components are not removed bytruncation during renormalization.

In Expression (14) for the collision operation, optionally, one or moreof the collision computing parameters: shift delay δ^(f); scaling vectorα ^(f); and phase shift φ^(f); are applied to the Zyoton frequencycomponents in the frequency domain. The superscript “f” indicates thatthe collision computing parameters are frequency-domain coefficients;and each Ω represents a frequency component undergoing interaction at atime point on the collision grid. Sorting the components of F′ (Z′) on adescending amplitude order yields the resulting magnitude spectrum ofthe modified Zyoton F′ (Z′).

As shown in the expression for F′(Z′), the collision computing parametershift delay δ^(f) is optionally introduced as an integer shift delay inthe index of the Zyoton components that interact with the components ofconditioned feature or modified zyoton. Values of δ^(f) can range from 0thru k−1 where k is the number of k-frequency components. As an example,shift delay δ^(f) may be used in Zyotons derived from waveforms such asparabolic-similaritons; wavelets; curvelets; ridgelets; or ellipticwaves, any of which can yield multiple components which are very closein frequency to each other, or yield groups of components that are closein frequency to each other.

With reference to FIG. 59A, the three k components of the Zyoton areclose in frequencies. The closeness for the delay shift operation neednot be determined by the ε_(k) test and, instead, another suitablethreshold such as frequency difference of no more than 0.2%, 0.5%, 1%,2% etc., of the larger or smaller frequency can be used to determine thecloseness. If such close frequency components are observed, thecollision process may start by setting the shifting value equal to thenumber of close components minus one. Thus, in the example shown in FIG.59A, δ=2. In one embodiment, the collision begins not with the componentZ1 , but with the component Z3. The bracket of the CF components to becollided with the component Z3, however, is not shifted. Instead, thecollision bracket for Z3 includes the CF components {CF1, CF2, CF3,CF4}. Once the value of the shift-delay δ is set, it is uniformlyapplied for all collision interactions. Thus, the collision bracket forthe Zyoton component Z8 includes the CF components {CF6, CF7, CF8, CF9}.

In some embodiments, the first of the close Zyoton components may beused and the remaining components or not used in the collision process.Instead, the collision continues with the next Zyoton component in theordered set that is not determined to be close in frequency. In someembodiments, the center component is selected and the remaining closecomponents are not used in the collision process. Here again, thecollision continues with the next Zyoton component in the ordered setthat is not determined to be close in frequency. For each of thesecollisions, the corresponding bracket of the CF components is shifted bythe delay-shift value δ. For example, FIG. 59B shows that the collisionof Z2, the center component, is performed using the bracket {CF1, CF2,CF3, CF4} and the next collision operation involves the Zyoton componentZ4, which is not close to Z1 , Z2, and Z3, and the collision bracket forZ4 is {CF2, CF3, CF4, CF5}. The center component can be determinedaccording to the frequencies of the close components or according to theamplitudes of the close components.

The phase shift φ^(f) shown in the expression for F′(Z′) can beintroduced, either as a constant phase shift (which reduces to a scalar)in the frequency domain; or as a rotation vector where the amplitude ofeach frequency component of the Zyoton Z_((g) _((t-δ) _(f) ₎ ₎participating in the collision is multiplied by a variable phase shiftcoefficient

$\phi_{g_{({t - \delta^{f}})}}^{f} = {\phi_{g_{({t - \delta^{f} - 1})}}^{f} + {\left( {t - \delta^{f}} \right)\frac{2\pi}{360*\left( {k + m + j} \right)}}}$${{where}\mspace{14mu}\phi_{1}^{f}} = {\frac{2\pi}{360*\left( {k + m + j} \right)}.}$

For subsequent (second and later) collisions, the frequency componentsof the conditioned feature would be replaced by the frequency componentsof the renormalized modified zyoton, and the other collision computingcoefficients would optionally remain unchanged. The expression can bewritten as:F′(Z″)=LI ₁ ^(K)(LI _(t-δ) ^(t-δ+CB)(α ^(F)(φ^(F)(Ω_(Z(g) _((t-δ) _(F) ₎₎))

Ω_(Z′(g) _((t)) ₎)),t=0,1, . . . ,(k+l+m)−1  (15)where Z″ is the new resulting modified zyoton, Z′ is the renormalizedmodified zyoton resulting from a previous collision, and other terms areas defined above.

Post collision, the sorted magnitude spectrum of modified zyoton F′ (Z′)would have more than k+m+j terms and would include any new frequenciescreated. For example, depending on the modality of the interaction, theco-product term of multiplying a frequency component of Zyoton Ω_(Z)with a corresponding frequency component of the conditioned featureΩ_(CF) could result in new frequency components with frequencies similarto those of the colliding entities, but with substantially reducedamplitudes compared to those of the original zyoton. When all theresulting frequency components are amplitude sort-ordered, the kfrequencies remain as the highest amplitude components, with thenewly-created frequencies appearing in lower energy bands.

The collision thus does not create new frequency components in theenergy range of the first k components of the modified Zyoton, and mayonly increase the collective spectral energy of those k components.Similarly, the forced frequency alignment described above, afterapplying a combination of delay, phase shift and scaling operations,ensures that no new frequency components, sort-ordered in the range oforiginal k components, are generated, because the new frequencycomponents generated by the modulation have amplitudes orderedsubstantially below the original k components. The new frequencycomponents generated by the collision process are removed by truncationof the amplitude-scaled frequency components as part of renormalization.

The different tests that are performed in the time domain and frequencydomain during various optional stages of collision between the Zyoton(Z) and conditioned features (CF), for all three of: the case of onespecific embodiment for non-invasive glucose; for embodiments foranalytes where the SCR, SNR, concentration, or intensity of signal maybe different from those in noninvasive glucose; and for otherembodiments only; are summarized in the table below.

TABLE 9 Embodiments for analytes with Glucose differing OtherOperation/Test Embodiment conditions embodiments Just prior tocollision, the Yes, but they can Yes, but they can Yes, but they canoriginal Zyoton (Z) and the also be represented also be represented alsobe represented conditioned feature (CF) are in the time domain in thetime domain in the time domain represented in the frequency domainCollisions are preferentially Yes Yes Yes performed in the frequencydomain, but can be described in the time domain. Collisions areperformed in the No, because Yes, but removal Yes. Can be used timedomain removal of certain of certain in systems with frequency frequencyhigh SNR, high components, e.g., components using SCR, systems with byusing filters, filters can lead to few frequency can lead to loss ofloss of numerical components (i.e., numerical accuracy, and loss k + j +m < 100), accuracy, and loss of accuracy of and/or Zyoton of accuracy ofinformation frequencies below information content, which can 1 KHz.content, which can cause the collision cause the collision computing tobe computing to be inaccurate. inaccurate. Performing collisioncomputing in the time domain can also be inefficient, because it isdifficult to ensure co-dependency conditions with low SNR and low SCR. Zand CF can be represented as Yes, but the two Yes, but the two Yes, butthe two time-domain waveforms. waveforms must waveforms must can havedifferent have the same have the same number of time number of points.number of points. points. Collision- computing parameters - delay- shiftand collision grid may be changed accordingly. Just prior to afrequency- Yes, and the Not necessarily, Not necessarily. domaincollision the spectral spectral energies this condition may energy of Zis designed to be are represented by not be required for much greater(e.g., 1,000 times) the frequency- all analytes. than the spectralenergy of CF domain amplitudes, i.e., the amplitudes of the frequencycomponents of the Z and CF. Just prior to the first frequency- Yes, butin this Yes Yes domain collision, a velocity test embodiment the isperformed and in which the CF is velocity of Z is scaled down andpreferentially not compared with the velocity of scaled. CF, or thevelocity of CF is scaled up and is compared with the velocity of Z Theabove test (kappa test) can Yes, by comparing Yes Yes be performed inthe frequency the amplitudes of domain the frequency components. If thetime domain kappa test No, failing the No, failing the No, failing theprior to the first collision fails, kappa test kappa test kappa test thevelocity of either Z, CF, or generally requires typically requires atypically requires a both, can be adjusted by scaling a redesigned Z orredesigned Z or redesigned Z or the frequency domain carrier kernel.carrier kernel. carrier kernel. amplitudes, so that the test passes.During a frequency-domain Yes, if it began Yes, if it began Yes, if itbegan collision, the spectral energy of with that spectral- with thatspectral- with that spectral- Z remains much greater (e.g., energyratio. energy ratio. energy ratio. 1,000 times, etc.) than the spectralenergy of CF, and of the renormalized modified zyoton that replaces theCF. Prior to the first frequency- Yes Yes Yes domain collision, anEpsilon Test is satisfied for all the k, m and j components individuallyand collectively. After the first collision a kappa Yes Yes, Yesvelocity test in the time domain (or a kappa spectral energy test in thefrequency domain) can be applied to the scaled Z and the renormalized,modified Zyoton Z″ If the test fails, the collision is Yes Yes Yesdiscarded and the process starts with a new original Zyoton Z or a newcarrier kernel. Post renormalization, and Yes. The Yes. The Yes. Theduring all subsequent frequencies of the frequencies of the frequenciesof the frequency-domain collisions, an k components are k components arek components are Epsilon Test must remain typically not typically nottypically not satisfied for all k components, changed by a changed by achanged by a individually and collectively. collision. New m collision.New m collision. New m and j frequency and j frequency and j frequencycomponents can be components can be components can be created. created.created. No new frequency components Yes Yes Yes in the amplitude rangeof the k components are created by a collision.

Iterative Collision Process

With reference to FIGS. 60A-60B, an original Zyoton (Z) is obtained froma synthesizer or a Zyoton database in step 2. In step 4, a co-dependentcarrier kernel (CK) is obtained from a synthesizer or a carrier kerneldatabase. A single database may store one or more Zyotons and one ormore carrier kernels. A feature (F1), generated as described above, isobtained in step 6 from a feature generator (described below). Thefeature may be optionally modulated by a pre-cursor modulating signal(e.g., a 16.5 Hz signal, a 50 Hz signal, a 1 kHz signal, a 100 kHzsignal, a 225 kHz signal, etc.). In step 8, the carrier kernel (CK) ismodulated using the feature F1, to obtain a conditioned feature (CF1).

In step 10 a Kappa test is performed to ensure that the original Zyoton(Z) and the conditioned feature (CF1) satisfy the co-dependency test. Toperform this test in the frequency domain, the scaled spectral energy atα_(t) ^(F)E(Z) of the original Zyoton may be compared with the spectralenergy of the conditioned feature E(CF1), where α_(t) ^(F) is thescaling coefficient. The superscript F identifies that this scalingcoefficient is applied in the frequency domain, and the subscript tindicates that this scaling coefficient is applied while performing atest. The properties of the actual waveforms Z and CF1 do not change byapplying this scaling coefficient. If the difference between the twospectral energies is less than or equal to a specified threshold κ, (asdescribed above), the co-dependency condition is satisfied. This testcan also be performed in the time domain, where Z and CF1 arerepresented as time-domain waveforms, and the velocities of the twotime-domain waveforms are computed. If the scaled velocity of theoriginal Zyoton and the velocity of the conditioned feature are within aspecified threshold, the co-dependency condition is satisfied.

If the Kappa test fails, the frequency domain amplitudes of the originalZyoton are actually scaled in step 12 according to a scaling factorα_(pc) ^(F), where the superscript F identifies again that this scalingfactor is applied in the frequency domain. The subscript pc indicatesthat this scaling factor is applied prior to the collision operation.The scaling factor α_(pc) ^(F) can change the frequency-domainamplitudes of one or more components of the original Zyoton Z.Alternatively, a scaling factor can be applied to the conditionedfeature. In some embodiments, both the conditioned feature and theoriginal Zyoton may be changed. Regardless of the waveform to which thescaling coefficient is applied, one or both waveforms Z and CF arescaled such that the Kappa test, i.e., the velocity test between theoriginal Zyoton Z and the conditioned feature CF1 is satisfied. In someembodiments, e.g., those in which the collisions are performed in thetime domain, a scaling factor is applied to one or both waveforms in thetime domain.

In some embodiments, a sensor provides a soliton based spectrum and thefeatures derived from such spectra are soliton based. In theseembodiments, precursor modulation is performed to modulate thesoliton-based features, e.g., using a modulating signal having afrequency of a few hertz, a few hundreds of hertz, a few kHz, a few MHz,or more. In some embodiments, these modulated features can be collideddirectly with a Zyoton, without generating a conditioned feature.Therefore, a Kappa test may be applied directly to the Zyoton and themodulated feature, to test co-dependency therebetween.

The Kappa parameter used in this testing, denoted κ_(F) is similar tothe parameter κ_(DV2) used in testing the co-dependency between a Zyotonand a conditioned feature. In performing this Kappa test, the velocityof the Zyoton and/or the velocity of the precursor-modulated feature maybe scaled. The Kappa test using the parameter κ_(F) can be performed inthe time domain or in the frequency domain. If this Kappa test fails,the frequency-domain amplitudes of the frequency components of theZyoton, the precursor-modulated feature, or both, may be scaled using ascaling coefficient α_(C), such that the Kappa test would succeed usingthe adjusted Zyoton and/or the precursor-modulated feature.

After the co-dependency condition is satisfied, the first collisioninteraction between the original Zyoton and the conditioned feature isperformed in step 14, which yields the first modified Zyoton Z1 ′. Asdescribed above, the collision operator also includes an optionalscaling operator. The collision interactions, as described above, cangenerate a modified Zyoton having frequency-domain amplitudes greaterthan the amplitudes of the Zyoton. Also, some of the frequency componentamplitudes of the Zyoton are significantly greater than some amplitudesof the conditioned feature due to scaling of the Zyoton relative to theconditioned feature prior to the collision. For example, in someembodiments spectral energy of Zyoton is set to be 10³ times relative tothe spectral energy of the conditioned feature which generally resultsin large scaling of frequency domain amplitudes of the modified Zyotonin the k-region. The scaling operator applied during the collisioninteractions scales the amplitudes to control the overall dynamic rangeof the amplitudes, so that a computer can perform the processingefficiently and with the required precision. Thus, the scaling operatoris customized to the computing apparatus and may adjust the waveformproperties primarily to facilitate computations using the selectedcomputing apparatus. The scaling factor α_(F) ^(pc) the other handactually adjusts the properties of the waveforms to be collided so thatthey become co-dependent.

After the first collision, whether the original Zyoton Z and the firstmodified Zyoton Z1 ′ are co-dependent is determined in step 16. In afrequency-domain implementation, the spectral energy of the originalZyoton E(Z) is scaled using a scaling factor {tilde over (α)}_(F) ^(t),and the scaled spectral energy is compared with the spectral energyE(Z′) of the first modified Zyoton. If the two energies are within theKappa threshold the first co-dependency condition, i.e., the velocitytest is satisfied. Similar to step 10, this test can be performed in thetime domain. The co-dependency also requires that the divergence of thepost-collision waveform, i.e., the first modified Zyoton Z1 ′, be withina specified threshold τ. This condition is also tested in the step 16.In some embodiments, the collision interactions and the Epsilon tests inparticular, can ensure that the divergence condition is satisfied and,as such, the divergence test is not performed explicitly in the step 16.If either test fails, it is determined that the selected Zyoton is notsuitable for collisions with the particular conditioned feature CF1.Therefore, a new original Zyoton may be selected in step 18, and thecollision process can restart from step 10, with the new originalZyoton.

If both the velocity and divergence tests succeed, the first modifiedZyoton Z1 ′ is renormalized in step 20. As described above,renormalization includes removing the energy of the original Zyoton froma modified Zyoton, which may be performed in step 22. Renormalizationmay also include truncating the modified Zyoton, and redistributing theaggregate energy of the components removed during truncation, among thesurviving m and j frequency components of the renormalized Zyoton, suchas the first renormalized Zyoton Z1 ″. Truncation and redistribution(also called amplitude balancing or rebalancing) may be performed instep 24. Either step 22 or 24 can be performed before the otherrenormalization step.

The renormalization process is controlled such that the energy of therenormalized Zyoton is on the scale of the energy of the conditionedfeature. The renormalized Zyoton is then collided again with theoriginal Zyoton in a subsequent collision iteration. Therefore, toensure the co-dependency between the first renormalized Zyoton Z1 ″ andthe original Zyoton Z, a Kappa test is applied to these two waveforms,in step 26. In the frequency domain, the scaled spectral energy of theoriginal Zyoton, α_(F) ^(t)E(Z) is compared with the spectral energy ofZ1 ″, denoted E(Z1 ″). If the absolute difference is less than theparameter κ, the next iteration of the collision may be performed. Thistest can also be performed in the time domain.

If the Kappa test fails, it is determined that the energy represented bythe conditioned feature CF1 cannot be extracted using the first originalZyoton Z; a new original Zyoton is selected in step 28. The collisioniteration may start again at step 10 using the new original Zyoton andthe conditioned feature CF1. If the Kappa test in step 26 succeeds, acollision interaction is performed in step 30 between the originalZyoton Z and the first renormalized Zyoton Z1 ″, which yields a secondmodified Zyoton Z2′. Whether the original Zyoton Z and the secondmodified Zyoton Z2′ are co-dependent is determined in step 32, similarlyas in the step 16. If one or both co-dependency tests fail, a neworiginal Zyoton may be selected in step 34, and the collision processmay restart from the step 10. Otherwise, i.e., if both co-dependencytests in step 32 succeed, the second modified Zyoton Z2′ may berenormalized in step 36. The step 36 is similar to the step 20, andincludes the energy removal step 38 and the truncation andredistribution step 40. The renormalization yields a second renormalizedZyoton Z2″.

In step 42, which is similar to the step 26, the co-dependency betweenthe original Zyoton Z and the second renormalized Zyoton Z″ is tested.If either or both tests fail, a new original Zyoton may be selected instep 44 and the overall collision process may restart in step 10.Otherwise, the next collision iteration (i.e., steps 30-42) may beperformed using the original Zyoton (Z) and the second renormalizedZyoton Z″. This iterative collision process may continue for thespecified number of iterations

, as described above.

Thereafter, in various embodiments, the renormalized spectral energygain of the renormalized Zyoton produced after the

iterations is computed. This energy gain generally corresponds to thespectral energy loss represented by the conditioned feature CF1, whichcorresponds to the energy absorbed by the analyte of interest and/or oneor more confounders in the wavelength range associated with the featureF1. The entire process 6000 may then be repeated with another feature F1that is matched with the feature F1, to compute the renormalizedspectral energy gain associated with F1 . The two energy gain values maybe used, as described above, to compute net renormalized spectral energygain (NRSEG) for the feature pair

F1, F1

. This overall process 6000 is typically repeated for different featurepairs. The original Zyoton used to collide with the two features of aparticular feature pair is generally the same. Different originalZyotons may be used, however, for different feature pairs.

System for Collision Computing

With reference to FIG. 61, a non-invasive measurement system or acollision-computing system 6100 includes a sensor 6102. The sensorincludes a radiation source 6104 and a detector 6106. The radiationsource 6104 can be selected according to the medium to be analyzed 6108and/or an analyte to be detected and/or quantitated. For example,in-vivo or in-vitro measurements of compounds such as glucose,cholesterol, etc., or for measurement of properties such as heart-beatrate, the radiation source 6104 can be an NIR radiation source. In othersituations, e.g., for detection/measurement of an atmospheric gas, theradiation source 6104 can be, e.g., an X-ray source, a gamma-ray source,an ultra-violet radiation source, a source of visible light, anacoustic/SONAR source, or an electromagnetic radiation source such as aRADAR. The detector 6106 is configured to receive the radiationreflected from and/or transmitted through the medium to be analyzed6108. The sensor 6102 also includes an analog-to-digital converter (ADC)6110, to convert the received radiation into a digital signal, alsocalled the sensor signal.

The sensor signal is received by a feature generator 6112, whichincludes a spectrum generator 6114. If the spectrometer is a Fouriertransform (FTIR) spectrometer, the spectrum generator may convert thefrequency components of the sensor signal, e.g., via an inverse Fouriertransform to a spectral signal or spectrum (e.g., intensity spectrum)corresponding to the sensor signal. In some embodiments, the spectrumgenerator 6114 may transform the initially generated spectrum into adifferent form. For example, an intensity spectrum may be transformedinto a corresponding absorbance spectrum. Typically, the intensity andabsorbance spectra represent absorption of the energy transmitted by theradiation source 6102 to the medium to be analyzed 6108 by an analyteand/or one or more confounders in the medium, and losses due toscattering.

The feature generator 6112 also includes a feature extractor 6116, whichdivides the spectrum generated by the spectrum generator 6114 into oneor more regions determined according to wavelength or wavenumber ranges.The individual portions of the spectrum corresponding to these region(s)are called features. The absorption of energy by the analyte and one ormore confounders may vary according to the wavelength of the incidentradiation and, as such, some features may represent strong absorption ofthe incident energy by the analyte relative to that by one or moreconfounders. Such features are generally called analyte features. Somefeatures may represent weak absorption of the incident energy by theanalyte relative to that by one or more confounders, and such featuresare generally called non-analyte features. The feature extractor 6116may generate one or more analyte features and one or more non-analytefeatures. In some embodiments, an optional pairing module 6118 pairs oneor more analyte features with a respective non-analyte feature.

The features are prepared for collision by the feature conditioner 6120,which may include a precursor modulator 6122 that modulates a featureusing a modulating signal (e.g., a waveform having a frequency of 16.5Hz, 1 kHz, 100 kHz, etc.) from a waveform database 6124. The modulator6126 receives a carrier kernel from the waveform database 6124 andmodulates the carrier kernel using a feature or a pre-modulated feature,to obtain a conditioned feature. As described above, each featurerepresents the energy absorbed by the analyte and/or one or moreconfounders, typically in the presence of noise and along withscattering losses, in the wavelength region associated with the feature.Therefore, the conditioned features derived from one or more featuresand one or more carrier kernels also generally represent the energyabsorbed by the analyte and/or one or more confounders, along with noiseand scattering losses, in corresponding wavelength regions.

The collision computer 6130 receives one or more conditioned featuresand one or more Zyotons from a Zyoton database 6132. In order to performa collision between a selected Zyoton and a conditioned feature, foreach frequency component of the selected Zyoton, the bracketed-collisionmodule 6134 performs the collision operations (e.g., the conditionalmultiplications of amplitudes, conditional sums of frequencies, andconditional sums of resulting amplitudes, as described above), usingfrequency components of the conditioned feature in the correspondingbracket thereof. After the collisions with a specified number of Zyotoncomponents are completed, a modified Zyoton is obtained which may berenormalized by the renormalization module 6136. Before, during, andafter the collision process one or more co-dependency tests (i.e., thevelocity (Kappa) tests and divergence (tau) tests) and Epsilon tests forcollision computations can be performed by the collision conditiontesting module 6138. The Epsilon tests may be performed by the bracketedcollision module 6134, as well. As described above, in variousembodiments, the operations of the bracketed collision module 6134 andthe renormalization module 6136 may be repeated for a specified numberof collision iterations. In general, a renormalized Zyoton may beiteratively collided with the original Zyoton or with a differentZyoton. Alternatively, a renormalized Zyoton may be collided with theconditioned feature.

After the specified number of collision iterations are completed, theprojector 6140 may receive one or more renormalized Zyotons. The NRSEGmodule 6142 may compute net, renormalized spectral energy gain (NRSEG)using the received renormalized Zyoton(s), which may correspond to pairsof features. The NRSEG module 6142 may also compute normalized NRSEGvalues, as described above. The AG module 6144 may compute absorptiongradients and normalized absorption gradients (NAGs) from the NRSEGvalues computed by the NRSEG module 6142. The projection conditionstesting module 6146 may test various conditions such as monotonicity ofthe computed NRSEG values across illumination states, etc. Based onthese tests, the NRSEG module 6142 and the AG module 6144 may reject oneor more feature pairs, as described below.

The quantitation module 6148 can receive a mapped projector curve setfrom a mapped projector curve set database 6150 and may use an NAG valueto select a suitable projector curve from the curve set. Thequantitation module 6148 may also use a normalized NRSEG value and theselected projector curve to determine a quantity (e.g., concentration)of the analyte of interest. Based on the measured quantity, thequantitation module 6148 can determine whether the analyte is present orabsent in the medium to be analyzed 618. For example, the analyte may bedetermined to be present if the analyte quantity or concentration isgreater than a specified threshold. Further details of the process ofprojection are described below.

The presence and the quantity can be presented to a user on a displaydevice 6160. The display can be in a binary form, such as “Detected” or“Not Detected;” “Yes/No;” or other suitable symbols. Additionally or inthe alternative, the display can indicate the measured quantity e.g., asan absolute value, a percentage, or a percentile rank. The display canalso indicate a concentration band such as a designated “High,”“Medium,” or “Low” band, a color code such as “Red,” “Yellow,” “Green,”corresponding to a concentration band etc. The number of concentrationbands can be two, three, five, seven, ten, etc.

In different embodiments, the various components of the non-invasivemeasurement system (the collision-computing system) 6100 may be includedin one or more physical units. In one embodiment, all system componentsare included in a single unit, such as a hand-held unit. With referenceto FIG. 62, the overall non-invasive measurement system 6200 includes afront-end module 6202 and a back-end module 6204. The front-end andback-end modules are in electronic communication with each other via anetwork 6206, such as a private, physical and/or wireless network, theInternet, and/or a combination thereof.

The front-end module 6202 includes the sensor 6102, the display 6160,and a transceiver 6262. The back-end module 6204 includes the featuregenerator 6112, the feature conditioner 6120, the collision computer6130, and the projector 6140. The back-end module 6204 also includes acommunications module (not shown). In this embodiment, the front-endmodule 6202 collects data from the medium to be analyzed 6108, transmitsit to the back-end module 6204 for processing of the collected data, anddisplays the received results. In the embodiment illustrated withreference to 6202, the overall system may be operated as a hostedservice, where the front-end module collects data and displays results,while the back-end module performs the operations necessary to obtainthe results.

With reference to FIG. 63, in another embodiment, a front-end module6202 includes the sensor 6102, the display 6160, the feature generator6112, the feature conditioner 6120, and the transceiver 6362. Theback-end module 6304 includes the collision computer 6130 and theprojector 6140, and also a communications module. In this embodiment,the front-end module 6302 collects data from the medium to be analyzed6108, generates conditioned features and transmits the conditionedfeature data to the back-end module 6304 via the network 6306 forprocessing of the conditioned features, and displays the receivedresults.

It should be understood that in various embodiments the non-invasivemeasurement system (the collision-computing system) 6300 may includemore than one front-end units and/or more than one back-end units, andthat other combinations of the various system components across thefront-end unit(s) and back-end unit(s) are possible. Any of these systemcomponents (except for the radiation source 6104 and the detector 6106)can be implemented using custom hardware, e.g., application-specificintegrated circuit(s) (ASIC(s)), field-programmable gate array(s)(FPGA(s)), etc.

Any of the components and sub-components of the non-invasive measurementsystem (the collision-computing system) 6100 (except for the radiationsource 6104 and the detector 6106) may also be implemented usingsoftware, such as embedded software and/or software that can bedownloaded, optionally compiled and/or interpreted, and executed on oneor more processors. One or more system components and sub-components canbe implemented in part using a hardware module and partially insoftware.

With reference to FIG. 64, a component (e.g., the feature conditioner6120) or a subcomponent (e.g., the bracketed collision module 6134, theAG module 6144, etc.) can be executed by a processing module 6402 havinga processor 6404 and a memory module 6406. The instructions to implementthe particular component or subcomponent may be stored in the memorymodule 6406. Such instructions can be pre-loaded in the memory module6406, or the processing module 6402 may receive such instructions fromthe server 6408. The server includes a processor 6410 and a memorymodule 6412. The processor 6410 may retrieve the instructions from thememory module 6412 and may transmit those instructions to the processingmodule 6402 via a network 6414.

In some embodiments, all operations of the component or the subcomponentmay be performed by the processor 6404. In some embodiments, theprocessor 6404 may transmit data to be processed to the server 6408 andthe processor 6410 may perform one or more of the operations associatedwith the component or the subcomponent to be implemented.

Zyoton and Carrier Kernel Synthesis System

The process of synthesizing the Zyotons and carrier kernels to be usedfor collision computing are described above with reference to FIGS.38-41. Some of the components of the non-invasive measurement system(the collision-computing system) 6100 (FIG. 61) are used to synthesizeZyotons and carrier kernels. With reference to FIG. 65, in the waveformsynthesis system 6500, the sensor module 6102 is used to obtainradiation corresponding to an analyte of interest from a controlledmedium 6502. In some embodiments, the controlled medium 6502 may includea diluting substance such as distilled water and a pre-measured quantityof the analyte. The spectrum generator 6114 of the feature generatormodule 6112 generates a pure component intensity or absorbance spectrumfor the analyte. The feature generator 6112 may generate one or morefeature pairs, for optionally determining the amplitudes of the highamplitude k components of a Zyoton. In some embodiments, the kcomponents have higher power than the m and j components.

The Zyoton component cardinality module 6504 determines the respectivecardinalities k, m, and j of the high, medium, and low energy componentsof a Zyoton. To this end, the Zyoton component cardinality module 6504includes a derivative generator 6506 that can generate first, second,and/or higher-order derivatives of a spectrum received from the featuregenerator 6112. The noise generator 6508 generates noise according tothe properties of the received spectrum and/or a derivative thereof, andthe mixer 6510 combines the spectrum and the noise to produce a noisysignal. The spectrum analyzer 6512 determines the frequency componentsof the noisy signal via Fourier analysis. The discriminant classifier6514 initially determines the number k of the high-energy componentsrequired in a Zyoton.

In a subsequent iteration, the controlled medium is modified to includepre-measured quantities of one or more confounders, and the processdescribed with reference to FIG. 40 is carried out using the sensor6102, the feature generator 6112 and the Zyoton component cardinalitymodule 6504, to determine the number m of the medium-energy componentsrequired in the Zyoton. In this iteration, the spectrum generator 6114provides a spectrum corresponding to pre-measured quantities of theanalyte and one or more confounders.

The controlled medium may then be modified to include a pre-measuredquantity of a dominant confounder, and the process described withreference to FIG. 41 is carried out using the sensor 6102, the featuregenerator 6112 and the Zyoton component cardinality module 6504, todetermine the number j of the low-energy components required in theZyoton. In this iteration, the spectrum generator 6114 provide aspectrum corresponding to pre-measured quantities of the analyte and oneor more confounders of which one is a dominant confounder.Alternatively, in some embodiments, instead of using a dominantconfounder, the noise generator 6508 generates noise as described withreference to step 16 of the process described using FIG. 41, and thenumber j of the low-energy components required in the Zyoton isdetermined.

After the cardinalities k, m, and j of the high, medium, and low energycomponents of the Zyoton are determined, various properties of the oneor more spectra generated by the spectrum generator 6114 and/orproperties of one or more noisy signals generated by the mixer 6510 areanalyzed by the spectrum analyzer 6512. Using these properties, such asbandwidth, amplitude distribution, etc., the Zyoton synthesizer 6520selects a suitable Zyoton family or a Zyoton generation function from adatabase 6522. If a Zyoton generation function is selected, a functiongenerator is used to generate the base Zyoton. Otherwise, the selectedZyoton family provides the base Zyoton. The base Zyoton provides thehigh, medium, and low-energy components, in terms of frequencies andamplitudes thereof, that can be included in the Zyoton to besynthesized.

The Zyoton synthesizer 6520 selects k high-energy components of the baseZyoton, m medium-energy components of the base Zyoton, and j low-energycomponents of the base Zyoton, to construct a new Zyoton. In someembodiments, the Zyoton synthesizer 6520 selects a number of features ofthe pure component analyte spectrum and the corresponding portions of aderivative of the pure component spectrum to compute the ratios of theamplitudes of the high-energy k components, as described above. TheZyoton synthesizer 6520 may then set or adjust the amplitudes of the oneor more k components of the Zyoton, and may also set or adjust theamplitudes of the one or more m components and/or one or more jcomponents of the Zyoton.

The carrier kernel synthesizer 6530 receives the values of thefrequencies of the k, m, and j Zyoton components and uses a waveformgenerator 6532 to generate frequency components at the receivedfrequencies. The carrier kernel synthesizer 6530 then sets or adjuststhe amplitudes of these frequency components such that the spectralenergy of the carrier kernel is approximately equal to a selectedfraction (e.g., 1/100; 1/500; 1/800; 1/1,000; 1/2,400; etc.) of thespectral energy of the Zyoton. In some embodiments, the carrier kernelsynthesizer 6530 may set or adjust the amplitudes of the frequencycomponents of the carrier kernel as a pre-selected fraction (e.g., 0.06,0.1, 0.15, 0.2, 0.23, 0.5, etc.) of the amplitudes of the correspondingcomponents of the Zyoton. The Zyoton synthesizer 6520 may store thesynthesized Zyoton in the Zyotons database 6540, and the carrier kernelsynthesizer 6530 may store the synthesized carrier kernel in the carrierkernels database 6542.

These waveforms can be used by a non-invasive measurement system (acollision-computing system), such as the system 6100 described abovewith reference to FIG. 61. Because some of the components of thenon-invasive measurement system (the collision-computing system) 6100(FIG. 61) are used for synthesizing Zyotons and carrier kernels, thesynthesized waveforms can account for one or more properties of thatsystem such as sensor noise, resolution, sensitivity, etc.

One or more components or sub-components of the waveform synthesissystem 6500 can be implemented using hardware, software, or acombination thereof, as described above in describing the system 6100.The software components can be implemented using a computer system suchas that described with reference to FIG. 64.

Mapped Projector Curve Set Generation System

Some of the components of the non-invasive measurement system (thecollision-computing system) 6100 (FIG. 61) can be used in a system forgenerating the initial unmapped projector curve set using a referencemedium (e.g., tissue phantom) and the projection sets using a measuredmedium (e.g., human subjects), and to map the projection sets onto theindividual projector curves. With reference to FIG. 66, the mappedprojector curve-set-generation system 6600 includes the sensor 6102, thefeature generator 6112, the feature conditioner 6118, and the collisioncomputer 6130. To facilitate operation of these components, the system6600 also includes the waveform database 6124 and the Zyoton database6132.

The sensor 6102 is used to obtain radiation from a reference medium 6602(e.g., tissue phantom), having a known quantity of analyte (e.g.,glucose). The projector curve set generator 6670 includes the NRSEGmodule 6142, which computes the NRSEG values corresponding to thereference concentrations of the analyte. After ensuring monotonicityacross illumination states and/or for different reference concentrationvalues, using the monotonicity testing module 6672, a relationshipbetween the NRSEG values and reference concentrations is determined bythe projector curve set generator 6670. This relationship can bedepicted as a composite curve. The projector curve set generator 6670can perform the change in slope analysis described above and generateindividual projector curves, as further described above. These unmappedindividual curves may be flipped as described above and stored in theunmapped projector curve set database 6674.

The sensor 6102 is also used to obtain radiation from a measured medium6604 having a known quantity of analyte (e.g., glucose). The measuredmedia can be one or more human subjects, where the analyte is measured,and the quantity thereof is thus known, using a reference system such asan invasive measurement system, in addition to measuring it with thenon-invasive measurement system 6100 (FIG. 61). The projection setmodule 6676 includes the AG module 6144 of 6100. The AG module is usedto compute absorption gains (AGs) or normalized absorption gains (NAGs)after optionally testing monotonicity of various NRSEG values acrossillumination states for one or more feature pairs using the monotonicitytesting module 6672.

The projection set module 6676 generates one or more projection setscorresponding to one or more ranges of analyte concentrations measuredusing the reference system. The projection set module 6676 also computesthe ranges of AGs/NAGs corresponding to each projection set (e.g.,minimum and maximum AG/NAG values for each projection set). Theprojection set module 6676 receives the unmapped flipped projector curveset, and the mapping module 6678 associates the computed AG/NAG rangeswith the corresponding individual projector curves, to produce a mappedprojector curve set. The projection set module 6676 may store the mappedprojector curve set in the mapped projector curve set database 6680.

The mapped projector curve set can be used by a non-invasive measurementsystem (a collision-computing system), such as the system 6100 describedabove with reference to FIG. 61 to quantitate and/or detect the analyteof interest via non-invasive measurements. One or more components orsub-components of the waveform synthesis system 6600 can be implementedusing hardware, software, or a combination thereof, as described abovein describing the system 6100. The software components can beimplemented using a computer system such as that described withreference to FIG. 64.

Measurement of Glucose in Tissue Using Near-Infrared Spectroscopy

Numerous attempts, as described above, have been made over severaldecades to measure glucose in tissue using measurements with opticalspectroscopic instrumentation, even including fiber optical sensingprobe variants with multiple sources and/or multiple detectors. Someapproaches used absorbance values in specific wavelength windows toattempt the separation of a glucose signal from confounders, withcorresponding data processing, while other approaches used entirespectral regions and a variety of multivariate data processingtechniques.

The collision computing approach described herein, however, rather thanattempting to separate the glucose signal from confounders using justabsorbance data and geometric variations in tissue, generallyaccumulates, post-acquisition, spectral energy changes from spectralregions, extracted via one or more collision iterations, and uses themto extract the signal due to glucose as distinct from that due to theconfounders. As described above, this is achieved, in part, by collidingonce or several times carefully modified spectral regions (conditionedfeatures) with selected waveforms having a certain propagation structureand that are unrelated to the data-acquisition domain (Zyotons) toisolate and amplify the spectral energy from different compounds,allowing an enhancement of signal to clutter (glucose to other absorbingmolecules). A mapping or projection of this analyte signal can yieldclinically accurate glucose measurements using the noninvasive system.Although the following example describes the noninvasive measurement ofglucose in tissue, as described below, data from other sources such asthose depicted in FIG. 67 can all be transformed so that they can beprocessed using a collision computer.

Near-Infrared (NIR) spectroscopy is one commonly used modality forcharacterization of organic and organometallic analytes, including thosefound in human tissue. When a sample is illuminated using near-infraredlight, this technique utilizes the measurement of intensity ofabsorption by molecules. As the wavelength of NIR absorption bands issomewhat separated for different types of chemical bonds, NIRspectroscopy can be used to estimate analytes in complex matrices withsome degree of selectivity. The absorption of NIR light as it passesthrough a medium to be analyzed such as human tissue, generally varieslinearly with the distance the light travels, denoted 1; with theconcentration of the absorbing substance, denoted C; and with ε, acharacteristic constant for each substance at a given wavelength (knownas the molar extinction or molar absorption coefficient).

The attenuation of NIR light due to a given material can be expressed bythe Beer-Lambert law, whereby the Absorbance A=log(I₀/I)=ε×C×l whereI_(o) represents the intensity of incident light and I denotes theintensity of the light transmitted through the medium. For example, if90% of the incident light is absorbed, and 10% is transmitted, theabsorbance is 1.0. A similar expression can be used for converting lightreflected by the medium, designated I_(r) to obtain a similar absorbancevalue, A=log(I₀/I_(r)). This quantity is formally designated“pseudo-absorbance,” but the use of the term “absorbance” to describethis quantity is in common use in near-infrared spectroscopy.

The propagation of NIR light in human tissue is generally attenuated bythe combination of absorption, scattering, and reflection of NIRphotons. Absorption and scatter in tissue are generally dependent on thewavelength, while reflection may depend on the angle between an incidentNIR light beam and a tissue surface, and differences in refractiveindices of the materials on either side of the interface. Absorption mayoccur variably at different wavelengths, depending on the molecularproperties of all substances in the light path.

When NIR light is scattered in tissue, the collisions between photonsand atoms, molecules, or physical structures in the tissue are elastic,implicating that no energy is lost due to the scattering event; thephoton merely changes direction. It should be understood that theelastic collisions in this context are the collisions between photonsand atoms/molecules in the tissue, and not between two co-dependentwaveforms. The direction in which a scattered photon travels isgenerally dependent upon the wavelength of the light and the size of thescattering particle. If the photon crosses a boundary where the twolayers have different refractive indices, the direction of travel of thephoton may be further altered.

A Beer-Lambert expression for a sample can be written by using theabsorption coefficients of all substances ε₁, ε₂, . . . , ε_(N) in thetissue in the travel path of NIR light, multiplied by the concentrationof each substance, as: A=(ε₁×C₁+ε₂×C₂+ε₃×C₃+ . . . +ε_(N)×C_(N))×l.However, as multiple photons are launched in a typical spectroscopicimaging system, the optical path length l is not the same for allphotons due to scattering. Also, the numbers of different molecules inthe tissue these photons may encounter cannot be accurately estimated,owing to spatial variations in the composition of tissue. In fact, as apractical matter, there is no unique path length through a scatteringmedium such as tissue, but a distribution of path lengths. The neteffect is that scattering both increases and broadens the range of pathlengths and thus the total attenuation (photon loss), leading to a riskof errors in analyte-specific absorption estimation.

Thus, deconvolution of total attenuation of light to analyte-specificabsorption generally cannot be accurately achieved, even with multiplemeasurements. This particularly applies to non-invasive spectroscopicmethods for tissue spectroscopy using different arrangements that mayinclude transmission-mode (using contralateral source-detectorconfiguration), and either a specular reflectance mode or adiffuse-reflectance mode (using ipsilateral source-detectorconfigurations). Inversion, i.e., the extraction of quantitativecomponent information of tissue spectroscopic data from the totalabsorption observed to the concentrations of components, is typically anill-posed, ill-conditioned problem and generally cannot be solved bylinear deconvolution methods, including a technique called matchedfiltering.

These problems are usually inherent to various types of spectrometers,including dispersive and interferometric NIR spectrometers. Otherchallenges stem from interference from confounders: other substanceswhich may be present in the same or significantly greater concentrationscompared to an analyte, may have the same or substantially higher molarabsorptivities, and may absorb in or around the same spectral region asthe analyte. The variable pathlength issue described above can also leadto unknown scattering losses. Because the water content of tissues istypically very high, and water is a very strong absorber in the NIR, theabsorption of water can have a particularly large optical effect, andsmall local variations in water concentrations, across even smalldistances in tissue, can lead to large absorbance errors relative to thetotal absorbance due to an analyte such as glucose.

When NIR light is directed at tissue, some light is reflected from thesurface in a process called specular reflection, and the amount of thisreflection is typically determined by the angle between the illuminationand the surface, and any differences in refractive indices at theinterface where the light is introduced to the tissue. Light whichpenetrates into a scattering medium such as tissue may be re-emitted bya process known as diffuse reflection, and the distribution ofre-emitted light may depend on the angle of illumination and the natureof the scattering medium. If the re-emitted light distribution intensitycorresponds to the cosine of the angle between the illumination and thesurface, the material is described as exhibiting Lambertian diffusereflection.

Various embodiments described herein facilitate the measurement ofclinical analytes generally known to be present in the blood,interstitial fluid, tissue, and cellular compartments, with a dynamicrange of concentrations from below picomoles/liter to tens ofmoles/liter. The techniques described herein can be applied to samplesin solid, liquid, or gas phases. Alternatively, or in addition,embodiments of the methods and systems described herein can be used toanalyze the blackbody thermal emission spectrum of tissue (in the mid-IRregion) to quantify the presence of glucose, where the spectrum isinfluenced by the tissue composition and the glucose concentration. Asin the case of absorption spectroscopy, the well-defined fingerprintspectrum of glucose in the mid-IR region may be confounded and modulatedby thermal emissions from other interfering substances and thebackground tissue thermal emission. Collision computing described hereincan nevertheless isolate the analyte (e.g., glucose) signal, i.e., theemission due to glucose as separated from both the emission due to theinterfering substances and background emission.

Clinical analytes may be analyzed in-vitro, using data derived fromobserving standard body fluids such as blood, urine, cerebral spinalfluid (CSF), sweat, saliva, tears, dialysate, synovial fluid, amnioticfluid, or cyst fluid. In-vitro analysis can be implemented onmeasurements made on exudates, internal secretions or transudates. Suchanalysis has significant clinical utility in areas such as screening,monitoring, diagnosing, therapy, remediation, transplantation andpersonalized outcome-focused coaching.

Various embodiments described herein can be used to characterizeclinical analytes in-vitro and/or in-vivo by analyzing data obtainedthrough spectroscopic measurement of, e.g., skin tissue. In-vivomeasurements can be obtained using sensors that make physical contactwith the skin, such as optical, electro-optical, electromagnetic,electrical, magnetic, radiological, or ultrasonic sensors; or in a“standoff” mode where the sensor does not make physical contact with theskin or tissue. Distances in standoff imaging may range from fewnanometers to a few meters.

Clinical measurements with high medical or therapeutic utility that canbe made using collision computing as implemented in various embodimentsinclude, but are not limited to: detecting the presence or absence of ananalyte; assessing the concentration of an analyte in an unknown sample;tracking and monitoring concentration changes of the analyte over time;comparing relative concentrations of the analyte across different areasof tissue, subjects and test populations; monitoring the instantaneousor time-averaged rate of change of analyte concentration; and measuringthe spontaneous depletion, spontaneous regeneration, forced depletion orforced replenishment of the analyte. During the process of measurement,a contacting sensor may alter the properties of the medium (e.g.,contact or pressure induced changes upon skin contact). Also, the mediummay be subject to external electromagnetic, magnetic, thermal, chemical,mechanical, vibration, external forces or stress which are typicallyobserved as coherent or non-coherent spectral noise or transients in thedata. Various embodiments described herein can account for thesevariations.

The generalized collision-computing process for spectroscopicnon-invasive determination of analyte concentration in a medium (e.g.,the glucose content of tissue) changes the old paradigm of classicalspectral feature analysis, which uses a variety of methods that aregenerally considered to be equivalent to computation of theFisher-information matrix, which may then be used to calculatecovariance matrices associated with a likelihood estimate. A Fisherinformation matrix may be used as a technique for selecting featuresfrom spectral data that carry information about the analyte.

In one sense, various known techniques can be described as “training bypriors,” such as using training data from human subjects, and thenapplying a “goodness of fit” or Fisher information metric that attemptsto minimize the variance expected value or other likelihood statistic ofthe observed information, to select one or more features to estimate theanalyte concentration. Fisher information is generally known in thefield of information theory as a method to measure the amount ofinformation that an observable (such as a spectral feature) carriesabout an unknown parameter of interest on which the characteristics ofthe feature depends. It is commonly defined and expressed as the“variance of the score,” or the expected value of the observedinformation. For a class of problems where the signal-to-noise orsignal-to-clutter ratio is below a threshold, the Fisher informationmetric, applied directly to observations, often yields sub-optimalobservable selection (e.g., the selection and length of spectralfeatures), and tends to be a poor predictor of the parameter of interest(e.g., glucose concentration in tissue).

To offset the limitation of classical Fisher information measures forspectral feature selection based on experimental “data from priors”(i.e., spectral measurements from human subjects with different glucoseconcentrations) a process of feature modulation, as described above, isused in various embodiments. The conventional “data from priors” processuses, in general, a trial selection of spectral features and algebraictransformations in an attempt to yield monotonic, consistentseparability of samples, as ordered by their analyte concentrationreference measurements in the Fisher information space. Instead, variousembodiments employing collision-computing can establish both theseparability and monotonicity of the modulated spectral features in theFisher information space. Initial feature sets may be selected based onknowledge of the absorption spectra of the analyte and known or expectedconfounders, and may be selected to include spectral regions of bothhigher analyte absorption and lower analyte absorption, as describedabove.

The procedure then can be summarized as follows: Select a carrier kernelsuch that when coupled with a feature, it can deliver an increase of upto three orders of magnitude in the amplitude of the analyte-informationrepresenting k frequency components (high amplitude components invarious embodiments) of a Fourier transformed feature after one or morecollisions, as described above. The selection of the carrier kernel isbased at least in part, on the frequency components of a spectral signalcorresponding to the analyte and/or first or higher-order derivativesthereof, typically with added noise. The expected analyte (e.g.,glucose) concentration range is implicitly used in the selection of thecarrier kernel, as the value of the variable k is set in variousembodiments by estimating the number of frequency components required toseparate higher and lower absorbance regions of the spectral signalcorresponding to the analyte, i.e., a transformed pure componentspectrum of the analyte, in the presence of up to three orders ofmagnitude added RMS random colored noise, as described above.Information about feature morphology, i.e., the frequency componentprofile of a feature, may also be used in synthesizing the carrierkernel, as described above.

In one embodiment for glucose measurement, a carrier kernel waveformincluded 128 frequency components in a frequency-domain representationthereof. Features from a set of ten optical spectra (acquired fromtissue phantoms with known glucose concentrations separated by about 40mg/dl), were used to modulate the selected carrier kernel waveform. Setswith concentration separation as low as to 10 mg/dl can optionally beused. A spectrum acquisition system with a spectral resolution of 2 cm⁻¹led to a candidate feature length of 8 cm⁻¹.

The Fisher information matrix was calculated using non-invasivelyacquired spectral data from human subjects participating in a clinicalstudy, with reference glucose values ranging from 50 mg/dl to 450 mg/dlas measured by a reference method. The observed Fisher informationmatrix (I) is the negative of the inverse of the expected value of theHessian matrix H, or I(Θ)=−H(Θ|Z_(n))⁻¹ where Θ is the observedparameter (e.g., reference glucose measurement) and Z is the set of nspectral feature observations in the dataset. Computation of the HessianMatrix can be performed using utilities in software packages such asMatlab™ and Mathematica™. The gradient of a Fisher vector (FV), computedfrom the Fisher information matrix, for tissue phantoms separated by 40mg/dl reference glucose concentration, can be used to separate thesamples of tissue phantoms.

If the separation of the gradients of the FV is less than a threshold(e.g., sec (π/9) radians, having a numerical value of 0.111111), it wasdetermined that Fisher information matrix failed to separate the tissuephantom samples. In that event, the feature length can be increased,e.g., doubled and/or the number of frequency components in the carrierkernel waveform can be increased, e.g., doubled. The increasing of thefeature length and the increasing of the carrier kernel waveformfrequency component may be performed in an alternating sequence.

If monotonicity of glucose concentration values determined via collisioncomputing with reference glucose concentrations is not achieved with acarrier kernel waveform of a selected size (e.g., the size in terms ofthe number of frequency components can be 512, 1000, 2048, 4000, etc.),and a selected feature length (e.g., 60 cm⁻¹), then the feature startlocation may be shifted e.g., by the smallest selected feature lengthsuch as 8 cm⁻¹ up to a maximum of 48 cm⁻¹ in either direction from theinitial feature start position. In some embodiments, a set of 22features with length of 60 cm⁻¹ and a carrier kernel waveform with 2048frequency components yielded acceptable separation results for a set oftissue phantoms with reference glucose concentrations separated by 40mg/dl.

Features may be selectively paired, for example, to emphasizedifferences between the spectral properties of the analyte and theconfounders, or to reflect differences in the level of absorption by theanalyte at different wavelength regions. Zyotons are generally chosenwith morphology such that their peak frequency component energy (i.e.,the spectral energy of the analyte-information representing kcomponents) is large enough so that when collided with a conditionedfeature derived from any of the selected data features, the Zyoton wouldbe perturbed but within limits specified by the dispersion velocity anddivergence parameters, as described above.

In some embodiments, a single carrier kernel is selected to be used forconditioning all features. The frequency-domain amplitudes of thefrequency components of the carrier kernel are scaled to establish thespectral energy of the conditioned feature waveform to be around1/1,000^(th) to 1/100,000^(th) (i.e., α_(Z)=0.001 to 0.00001, asdescribed above) of the spectral energy of the Zyoton. After theselected carrier kernel is modulated by the features, a test may beperformed to determine if collisions performed using the Zyoton and theconditioned features can separate the spectral energy levels between twoor more tissue phantom samples with known differing levels of analyteconcentration. If the separation cannot be achieved, a new carrierkernel waveform may be selected or synthesized. In some embodiments, fordifferent features, different carrier kernel waveforms are selected andare paired with different Zyotons, according to the general selectionprocess described herein.

During a selected number of collisions, first between a Zyoton and theconditioned feature, and then between the renormalized Zyoton (obtainedby renormalizing the resulting waveform from the collision called themodified Zyoton) and the original or another Zyoton, the spectral energyof the modified Zyoton and/or the renormalized Zyoton is tested todetermine if the energy of selected frequency components of the waveformafter each collision iteration (or at least a specified number ofcollision iterations such as 2, 3, 5, 6, 10, 25 etc.) is changing (i.e.,increasing or decreasing) in a monotonic fashion. If this monotonicityis not achieved, a new Zyoton (and/or a new carrier kernel) may beselected and the monotonicity test (and the separation test if a newcarrier kernel waveform is selected) may be repeated. When themonotonicity condition is met, and a selected number of collisionsbetween the Zyoton and the conditioned feature are completed, thespectral energy of the final waveform, i.e., the final renormalizedZyoton is used in various embodiments to determine the presence orabsence of the analyte or to calculate the analyte concentration, or achange in the concentration.

In spectral signals obtained from NIR radiation received from a tissuesample, the energy loss due to the analyte is typically much less thanthat due to one or more confounders, and the total energy losses due tothe analyte and confounders are often significantly less than the lossdue to scattering and/or dispersion of the radiation in the tissue. Assuch, the signal-to-clutter ratio (SCR) of a signal corresponding to theenergy loss due to the analyte of interest to the overall energy lossdue to confounders and scattering can be very low, e.g., often as smallas 1×10⁻⁶. By tuning one or more of the Zyotons, the collision operator,one or more parameters thereof, and the carrier kernel waveformmodulated by the feature, to an expected required SCR increase, theenergy loss represented by the feature can be amplified withoutintroducing noise and/or distortion in one or more collision iterations,and can thus be measured.

One objective of the Zyoton tuning process is to configure the Zyotonsuch that energy loss estimated from a Zyoton collided with a specificconditioned feature, after one or more selected number of collisioniterations as described above, is monotonically increasing, that is,unidirectional with the concentration of analyte in the sample, asmeasured by a reference system, over the analyte concentration range ofinterest, when the analyte concentrations and measured energy loss arerepresented as ordered pairs. The collision process can be thusdescribed as a monotonic transformation of an acquired spectroscopicdataset. A calibration table, curve, or set of curves can be used todetermine accurately the concentration of the analyte in the medium tobe analyzed according to the amplified energy loss or gain, asrepresented by the final result of one or more valid collisions, wherethe validity of the collision iterations can be verified bymonotonicity, as described above.

The collision process is not only used to assess absorption energychanges in the NIR band due to analyte presence but also to deconvolvethose energy changes from attenuation due to scattering losses resultingfrom the medium and absorption from confounder molecules. A singlecollision iteration may be adequate to deconvolve these changes withhigh confidence in some situations. Many situations typically requireseveral (e.g., 10; 100; 500; 1000; 2000; 10,000; 100,000; or more)collision iterations. By varying the phase of one or more of thefrequency components of one of the colliding entities, e.g., a Zyoton,in each successive collision, artifacts due to random noise, instrumentdrift and instabilities, sampling errors, and ambient conditions can befiltered out. The phase operator may be applied in the time domain orfrequency domain. In the frequency domain phase changes are introducedas scaling of frequency components in the collision step. Also, severalcollisions can be used to expand the dynamic range of estimated spectralenergy changes so that greater precision can be obtained during thepost-collision projection process for estimating the analyteconcentration. In a sequence of several (e.g.,

) collisions of well-designed entities, the renormalized energy gainincreases (or energy loss decreases) monotonically over a subsequence ofsuccessive collision iterations of a specified cardinality n, where 2≦n≦

. At the end of the

collisions, a cumulative net, positive gain or loss is achieved invarious embodiments.

Utility can be optionally derived from the use of a single collisioniteration. For example, while accurate glucose concentrations aretypically not easily determined with a single collision iteration, theglucose range can be classified in a “glycemic wellness” application foran individual as “low,” where the glucose level is approximately below80 mg/dl, “normal,” where the glucose level is approximately between 80mg/dl and 180 mg/dl, or “high,” where the tissue glucose isapproximately over 180 mg/dl. The net, renormalized spectral energy gainobtained after a single collision iteration can be used to classify thetissue glucose in such a glycemic wellness regime.

Different Zyotons may be used to collide with different conditionedfeatures. As described above, different features extracted from spectralregions where analyte absorption occurs relatively strongly and regionswhere absorption occurs more minimally can have large differences on theabsorbance scale. These differences for analytes of interest can varyover several orders of magnitude. With such variances in absorptionproperties, the co-dependency condition cannot be easily achieved usingthe same Zyoton for all features. Thus, in some embodiments, differentZyotons are designed and tested to ensure that each conditioned featureand Zyoton pair satisfies the co-dependency condition described above.As also described above, the classification of features into “stronglyabsorbing” and “minimally absorbing” regions is only approximate. Insome cases, the features represented as being from “minimally absorbingregions” may be from regions that correspond to substantial analyteabsorption but which also correspond to substantial absorption fromconfounders.

By absorbing radiation, the analyte in the medium generally causes achange in the amount of radiation reflected by the medium or transmittedtherethrough relative to the radiation that would be reflected ortransmitted therethrough if no analyte were present in the medium. Thischange is generally represented in the acquired spectral data of themedium and, hence, in one or more extracted features, but is usuallyhidden in frequency components of extremely low amplitude. The Zyotons,the conditioning of the features, and the collision operator areconstructed such that one or more collisions generally induce ameasurable change in one or more properties (e.g., the spectral energyloss due to absorption of the incident light/radiation by the analyte inthe selected NIR spectral bandwidth) of portions of the waveformresulting from the collisions. After a preset number of collisionsbetween a conditioned feature and the corresponding Zyoton have beencompleted, as described above, such change in the resulting waveform ismeasured to determine the net spectral energy gain/loss due to eachconditioned and collided feature.

In various embodiments, during a collision process involving one or morecollisions, the changes in the properties of the Zyoton waveform beforeand after collision are analyzed as a mechanism to infer properties ofthe feature. As described above, impacted properties include changes inpropagation velocity, peak energy, dispersion velocity and changes inthe spectral envelope as represented, at least in part, by divergenceand/or a change in the time-domain length of the waveform or the numberof frequency components therein. These changes are quantified throughmeasurement of changes in the spectral energy of the resulting waveformafter each collision, the difference being that in the first collisionthe conditioned feature waveform and Zyoton waveforms collide, and insubsequent collision the Zyoton collides with the renormalized result ofthe prior collision, which includes the effect of the feature.

In effect, the process examines how the conditioned feature alters theproperties of the Zyoton waveform, i.e., the collision yields changes inthe energy of the Zyoton waveform. Depending on how the conditionedfeature waveform itself has been influenced by the underlying analyteabsorption, and by absorption and scattering due to confounders and themedium to be analyzed, the impact on the Zyoton can be different. AZyoton can thus be described as a nonlinear amplifier system and afeature as a perturbation. In general, the iterative collision processis thus a protocol for characterizing analyte properties and estimatinganalyte concentration in uncharacterized samples.

One specific embodiment of a non-invasive measurement system employingcollision computing generally described above is now discussed fornon-invasive glucose detection and measurement in human tissue usingdiffuse reflectance NIR spectroscopy, where the radiation sources anddetectors are both in contact with the skin. The distances of differentsources from one or more detectors are different and, as such, thisapproach can be called “tomographic spectroscopy.”

For non-invasive measurement of an analyte using spectral absorption intissue in the NIR region, the presence and/or concentration of theanalyte can be determined by using the collision process describedherein to estimate the net photon energy losses due to absorption by theanalyte molecules. The energy losses due to the confounders can besignificantly larger (e.g., two, three, five times, etc., or even one tofour orders of magnitude larger) than the energy absorbed by the analyteof interest. The scattering losses can also be high, often more thantwo, four, ten, etc., orders of magnitude greater than the energyabsorbed by the analyte. For example, for non-invasive measurement ofblood glucose concentration, empirical measurements and bio-opticalsimulation models for skin and sub-cutaneous tissue show that over 99.9%of photon energy losses are due to scattering and due to absorption frommolecules other than glucose. The mechanism of scattering and scatteringlosses were described above. The scattering losses generally depend onthe attenuation coefficient for the medium, and the wavelength ofincident light.

This embodiment employing collision computing exploits three fundamentaldifferences in scattering and absorption losses during light propagationthrough tissues: First, human skin has a layered structure, and thereare well-understood compositional differences in the near-surface skintissue layers. For example, the epidermis or outer layer has largeamounts of protein but is generally lacking in glucose, the intermediatedermis layer has larger amounts of glucose, the lower subcutaneous layerhas a preponderance of fats, and the different layers have varyingprotein structures present. Thus, both scattering and absorptionproperties are different for the different layers. By designing animaging strategy and combining features obtained from the measuredspectra that target different tissue layers, absorption and scatteringeffects were separated on a per-layer basis.

Second, each chemical compound has a wavelength-specific characteristic“fingerprint” or spectral signature. However, in the near-infraredregion, these spectral signatures are often not distinctive because theabsorption bands are broad and overlap frequently. Scattering andabsorption energy losses from other compounds can create intensitychanges in the same regions as the analyte, thereby further obscuringthe analyte absorption signal. Collision computing generally allows forrecapturing a weak signal where such a spectral fingerprint is availablebut cannot be clearly distinguished from other substances usingconventional techniques. A pathological case is where other substanceshave the identical spectroscopic fingerprint as glucose and are presentin substantial concentrations. The two may then becomeindistinguishable. However, there are no known substances with identicalabsorption profiles present in concentrations high enough to causesignificant errors in the measurement of glucose in the tissue layersinterrogated using the spectroscopic tomographic process describedabove, thereby rendering this technique generally applicable to thepractical, non-pathological situations.

Third, the wavelength dependency of scattering in human tissue islargely different from the absorption profile. Scattering losses followa different mechanism, having values that generally increase withdecreasing wavelength. This property is generally in effect at thefeature level and generally applies to all features. In variousembodiments, the Zyoton waveforms are synthesized with the ability toseparate wavelength-dependent attenuation from the patterned attenuationof absorption, which can allow for elimination of this major source ofclutter.

Post-processing of collision results from all features and all tissuecompartments focuses on exploitation of the first and second propertiesdescribed above. Also, the scattering properties of the various tissuecompartments are generally dependent on both time and physiology, andcannot be accurately estimated in many situations. However, thedistribution for scattering attenuation typically follows a normaldistribution, and this normal distribution manifests in the spectra asrandom noise. The parameters of the distribution can be different ineach layer and among different subjects. The generalized collisionprotocol, specifically with the variations in phase and delay for thecollision operator described above, can overcome these sample-to-sampledifferences in scattering that may manifest as random noise artifacts.

In various embodiments, in order to measure the analyte concentrationaccurately, a three step process is used, where each step may employcollision computing: (i) estimation of the net energy absorbed in eachextracted feature due to analyte presence; (ii) net energy absorbed inall the features from a single spectrum acquired during a multipleillumination sequence (MIS) (as described below), and; (iii) the netenergy absorbed, as estimated from multiple spectra acquiredcorresponding to each illumination state in an MIS (all the spectraacquired may be employed).

As described here and below, in some embodiments, an illumination stateis implemented by turning on several sets of illumination sources (eachset corresponding to a particular illumination state), geometricallyarranged in concentric rings around a detector. Let the simultaneousturn-on condition of one or more illuminators in a set (e.g., individualilluminators in a ring; groups of illuminators in one or more rings; allilluminators in a ring; or all illuminators in multiple rings),correspond to an “illumination state,” denoted R_(t). Furthermore, anillumination sequence is designated as I¹, I², and I³, where each I^(n),i.e., an illumination state, can be any combination of simultaneousturn-on of one or more rings (sets of illumination sources, in general).

In one example, features F1 and F2 were captured and selected fromreflectance spectra acquired corresponding to each illumination stateI^(n) during an illumination sequence, having three illumination states.In this example, step (i) described above involves the determination ofΔe corresponding to F1 or F2 based on each I^(n), i.e., based on Δe₁ ¹,Δe₁ ², and Δe₁ ³ or based on Δe₂ ¹, Δ₂ ², and Δ₂ ³. In some embodiments,the determination of Δe requires analysis of a feature pair. In suchembodiments, the determination of Δe may be based on any one featurepair but not on all feature pairs in step (i).

Step (ii) described above involves the determination of Δe (Δe₁ ¹+Δe₂¹), i.e., energy corresponding to illumination state I¹ and bothfeatures F1 and F2; (Δe₁ ²+Δe₂ ²); and (Δe₁ ³+Δ₂ ³). If additionalfeatures are available, they may also be used in the determination ofΔe. Step (iii) involves the determination of Δe using ΔE¹, ΔE², and ΔE³,where ΔE^(n) is the energy change absorbed using two or more spectracorresponding to two or more repeats of at least one of the illuminationstates (i.e., I^(n), where n=3, in this example) for each feature (i.e.,F1 and F2 in this example). In different embodiments, ΔE^(n) canrepresent an aggregate or an average of the energies computed for therepeats of a particular illumination state I^(n). For simplicity, thenumerical value of the net, renormalized, spectral energy gain that isdescribed in detail below, for a “feature pair” is referred to as“NRSEG.” In some embodiments, the NRSEG can be a value less than zero,where collision iteration(s) are constructed to produce modifiedZyoton(s) that have less spectral energy than the original Zyoton.

Illumination sequences are often useful because the resulting NRSEGs canbe used to directly generate additional metabolic, clinical, andanatomical attributes. For example, NRSEG obtained from an illuminationsequence for non-invasive glucose detection also enables identificationof non-glucose containing tissue such as the stratum corneum layer andrejection of unsuitable samples. With this approach, spectroscopicmeasurements from the palm of the hand may be rejected if the skintissue contained an unusually thick stratum corneum layer.

The post-collision Δe term corresponds to the net energy absorbed by theanalyte in the features. Also, a distinction between steps (ii) and(iii) is as follows: Step (ii) involves a single spectrum for eachillumination state. For example, if the sequence is (R1), (R1+R3), (R3),and (ALL Rings) (where R1 stands for Ring 1, R2 stands for Ring 2,etc.), for each illumination state in this sequence, only one spectrumis collected while performing Step (ii) and in computing the energies inthat step. However, while performing Step (iii) and in computing theassociated energies, optionally multiple spectra are acquired for eachillumination state. For example, ten spectra for each of (R1), (R1+R3),(R3), and (ALL Rings). Either the spectral intensities or the spectralabsorbances can be added and averaged for the entire spectra, or eachspectrum can be deconstructed into features, and then Δe computed foreach feature, after which all Δes can be averaged.

The process of analyte estimation may additionally include a spectrumstandardization step for compensating variability due to the opticalsampling process, ambient factors (e.g., temperature, humidity) that mayimpact analyte absorption, and variability in optical coupling betweenthe optical sensor/detector and the medium. In non-invasive analytemeasurement using spectra obtained by NIR illumination of skin,normalization may also be provided for variability in tissue hydration(a strong spectral confounder), variability due to demographicdifferences such as age, sex, skin pigmentation, skin thickness, skintopography, and fat content, and sampling inconsistencies due tovariability in sensor contact with the skin.

Using a spectroscopic measurement system such as that shown in FIGS. 68through 70, with several illumination states, normalization may beperformed through a differential comparison of spatially resolvedspectral measurements from different rings. In one example, thedifference between two different ring absorbance measurements isutilized and optionally ratioed, wavelength by wavelength, to a thirdring or to “ALL Rings.” Another normalization procedure may utilizemultiplicative scatter correction which may be windowed over selectivewavelength ranges, across all the illuminations in an MIS, to provide aset of template spectra representative of a calibration data set, asdescribed below.

Creation of a Calibration Curve Set with Tissue Phantoms

Synthetic media called tissue phantoms are engineered, calibrated,time-stable, tissue-like materials for calibrating, comparing andassessing NIR spectroscopic imaging system performance. The bulk phantommaterial may include, for example, gelatin, Intralipid (a syntheticemulsion of triglycerides in water that mimics the scattering propertiesof tissue), polystyrene beads of defined size and optical properties,and application-specific compounds. Well engineered tissue phantoms havevariability, absorption, and scattering bulk properties comparable tothose observed when imaging human tissue with the same instrument. Inorder to use these phantoms as part of a calibration set, it isimportant that the scattering and absorption properties of the tissuephantom match reasonably well those of the actual medium in which theanalyte concentration is to be measured, such as human tissue.Concentrations of known confounders in these phantoms typically rangefrom zero to twice their highest anticipated concentration in actualtissue, with the exception of water, which in tissue is often close toits maximum concentration. Each different concentration level of theanalyte of interest and confounders defines an independent, uniquesample.

Thus, predefined absorbance and scatter properties can be constructed ina volume of liquid or solid material, and complex tissue phantoms can beconstructed to capture variations of analyte concentration, tissuelayering and optical properties. A calibrated set of tissue phantoms,each with a representative reference glucose concentration measurementto assess monotonicity of estimated spectral energy gains due to glucoseabsorption with concentration, may be used in Zyoton design, asdescribed above, and in calibration and optimization for non-invasiveglucose measurement at the desired precision and accuracy.

In an embodiment for the noninvasive measurement of glucose in tissue,analyte detection and quantitation estimation is made on the basis ofcomputing the net relative perturbation in the renormalized spectralenergy gain of the Zyoton waveform resulting from collisions with eachfeature extracted from a spectral region corresponding to relativelystrong glucose absorption (“GL features”), compared to the perturbationin the renormalized spectral energy gain of the same Zyoton waveformresulting from collisions with a different spectral feature extractedfrom a region corresponding to less strong glucose absorption(“NO-GLfeatures”). In other embodiments, for other analytes of interest,a similar process is employed with respect to feature(s) extracted fromspectral region(s) corresponding to relatively strong analyteabsorption, called analyte feature(s), and feature(s) extracted fromspectral region(s) corresponding to relatively less strong glucoseabsorption, called non-analyte feature(s).

This process may be repeated for each illumination state. As the analyteabsorption and scattering in human skin tissue are both known to bepathlength and wavelength dependent, and different GL and NO-GL featuresrepresent different average levels of analyte absorbance, theirrenormalized spectral energy gain aggregated over the

collisions is further standardized in this embodiment to obtain the net,renormalized spectral energy gain (NRSEG).

This standardization can be achieved by colliding the Zyoton with thecarrier kernel γ, frequency modulated by the same frequency (e.g., 16.5Hz or 100 KHz in specific embodiments) used to modulate the GL and NO-GLfeatures, but without the use of any feature data. As described above,only the amplitudes from the k frequency components are used in thespectral energy computations in some embodiments. Thus, the NRSEG due toanalyte (e.g., glucose) presence is given by:

Δ ⁢ ⁢ e → ( GL F p , NO - GL Fq , Z r , R t ) = Δ ⁢ e ⇀ ( GL F p , Z r , Rt ) / Δ ⁢ ⁢ e → ( NO - GL Fq , Z r , R t ) ( GL F p , Z r , R t ) / Δ ⁢ ⁢ e→ ( Υ , Z r , R t ) ( 16 )where the term

$\Delta\;{\overset{\rightarrow}{e}}_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},{Z_{r}.R_{t}}})}$represents the relative renormalized spectral energy gain of the Zyotonwaveform (Z_(r)) resulting from collisions (with a collision iterationcount of

) with a conditioned feature extracted from the analyte-absorbing regionof the acquired spectrum (e.g., GL_(F) _(p) ) vis-à-vis the renormalizedspectral energy gain of the same Zyoton waveform, (Z_(r)), resultingfrom collisions with a different feature extracted from a region knownto be minimally absorbing (i.e., NO-GL_(F) _(q) ), for each illuminationstate.

As described above, an illumination state generally representssimultaneous turn-on condition for all the separate illumination sourcesin an entire illumination set (ring or rings), R_(t), where t=1, 2, 3,4, 5, 6, or “ALL Rings” (where “ALL Rings” corresponds to illuminatingall rings at the same time, e.g., 6 in a 6-ring illumination system),for illuminators similar to those shown in FIGS. 68 through 70. Toreemphasize, “illumination state” is generally expressed in terms ofwhich rings are illuminated. An illumination sequence (also calledmultiple illumination sequence (MIS)), is a sequence [R_(t)], ofmultiple illumination states, R_(t), where an illumination state can bean illumination of a single ring or the illumination of two or morerings. For example, [R_(t)] can be:(R1),(R2),(R3),(R5),(ALL); or

$\left( {I^{1}\overset{\Delta}{=}{R\; 1}} \right),\left( {I^{2}\overset{\Delta}{=}{{R\; 2} + {R\; 3}}} \right),\left( {I^{3}\overset{\Delta}{=}{{R\; 4} + {R\; 5}}} \right),\left( {I^{4}\overset{\Delta}{=}{R\; 5}} \right),{\left( {I^{5}\overset{\Delta}{=}{ALL}} \right).}$

The number of unique illumination states is denoted M. One or moreillumination states may be replicated, as described below. In either ofthe two examples above, M=5, including the illumination state ALL rings.In general, M can be less than or greater than 5. In a differentembodiment, where only three rings of illumination are used, theIllumination States in the MIS could be described as R1, R2, R3, and“All Rings,” and M would equal 4.

An example of paired features GL_(F) _(p) , NO-GL_(F) _(q) is GL−1,NOGL−1, as defined in FIG. 49; and, the corresponding zyoton Z_(r) givenby Z-kernel-E1, Z-kernel-D1, Z-kernel-S1, and Z-kernel-MM1,corresponding to the illumination states of rings R1, R2, R3, and ALLRings.

In Equation (16) the term

$\Delta\;{\overset{\rightharpoonup}{e}}_{({{GL}_{F_{p}},Z_{r},R_{t}})}$represents the renormalized spectral energy gain of the zyoton waveform(Z_(r)) resulting from collisions (with a collision count

) with a conditioned feature extracted from the analyte-absorbing regionof the acquired spectrum, e.g., (GL_(F) _(p) ). The symbol “Δ{rightarrow over (e)}” indicates a vector over R_(t)=1, 2, 3, ALL. The term

$\Delta\;{\overset{\rightharpoonup}{e}}_{({{GL}_{F_{p}},Z_{r},R_{t}})}$is computed using the results of applying the collision-operator(defined above) as Ω(GL_(F) _(p) ,Z_(r) )_(t) _(l) over

collisions.

The term

$\Delta\;{\overset{\rightharpoonup}{e}}_{({{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}$is the cumulative renormalized spectral energy gain of the same zyotonwaveform, (Z_(r)), resulting from collisions with a differentconditioned feature extracted from a region known to be minimallyabsorbing (i.e., NO-GL_(F) _(q) ), and

$\Delta\;{\overset{\rightharpoonup}{e}}_{({{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}$

is computed using the results of applying the collision-operator(defined above) Ω(NO-GL_(F) _(q) , Z_(r) )_(t) _(n) over n=1, . . . ,

collisions.

The term

( NO - GL F p , Z r , R t )in Equation (16) represents the renormalized spectral energy gain of thezyoton waveform (Z_(r)) resulting from the first collision with aconditioned feature extracted from the minimally analyte-absorbingregion of the acquired spectrum, e.g., (NO-GL_(F) _(p) ). Thus, in theunique case in which only one collision is used, the equation abovesimplifies to:

$\begin{matrix}{{\Delta\;{\overset{\rightarrow}{e}}_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}} = \frac{\Delta\;{\overset{\rightharpoonup}{e}}_{({{GL}_{F_{p}},Z_{r},R_{t}}\;)}}{\Delta\;{{\overset{\rightharpoonup}{e}}_{{({{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}^{2}}/\Delta}\;{\overset{\rightharpoonup}{e}}_{({\Upsilon,Z_{r}})}}} & (17)\end{matrix}$

The term Δ{right arrow over (e)}_((Υ, Z) _(r) _(, R) _(t) ₎ is therenormalized spectral energy gain of the same zyoton waveform, (Z_(r)),due to collisions with the carrier kernel Υ, that has been frequencymodulated, in the same manner as the GL and NO-GL features. No featuredata are used in this computation of Δ{right arrow over (e)}_((Υ, Z)_(r) _(, R) _(t) ₎. Therefore, this term is independent of R_(t) and, infact, is generally constant across all values of R_(t). This term iscomputed using the results of applying the collision-operator (definedabove) Ω(Υ, Z_(r) )_(t) _(l) over l=1, . . . ,

collisions.

In various embodiments, this term

$\Delta\;{\overset{\rightarrow}{e}}_{{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})},}$i.e., the NRSEG due to analyte absorption, is computed for all (p, q)pairings of GL-p and NO-GL-q features exemplified in FIG. 49, for aparticular illumination state R_(t), where t=1, 2, 3 or ALL Rings (as inthis example). The computation for all feature pairings is then repeatedin some embodiments for all illumination states.

Optionally, if the signal-to-clutter (SCR) ratio is relatively high,e.g., above 0.1, features need not be selectively paired with otherfeatures (e.g., from wavelength regions of differing absorption) tocompute the post-collision net renormalized spectral energy gain.Therefore, in some embodiments, the post-collision results of theanalyte and non-analyte features (e.g., the GL and NO-GL features asshown in FIG. 49) are not paired. Examples of applications whererelatively high SCR may be encountered include in-vitro analysis ofblood or body fluid analytes where the samples to be analyzed have beenpre-amplified using biochemical assays, or blood analysis usingfluorescence assays using detection techniques such as high affinityfluorescence tags. In-vivo examples include analysis of data frominvasive, implanted fluorescence tags. Thus, the NRSEG Δ{right arrowover (e)}_((F) _(p) _(R) _(t) ₎ due to analyte presence in a featureF_(p) for an illumination state R_(t) can be computed using:

$\begin{matrix}{{\Delta\;{\overset{\rightarrow}{e}}_{({F_{p},R_{t}})}} = \frac{\Delta\;{\overset{\rightharpoonup}{e}}_{({F_{p},Z_{r},R_{t}}\;)}}{\Delta\;{\overset{\rightharpoonup}{e}}_{({\Upsilon,Z_{r},R_{t}})}}} & (18)\end{matrix}$where the terms Δ{right arrow over (e)}_((F) _(p) _(,Z) _(r) _(,R) _(t)₎ and Δ{right arrow over (e)}_((Υ,Z) _(r) _(,R) _(t) ₎ are describedabove.

In spectroscopic systems constructed using multiple sources and singledetection element or single illumination element and multiple detectionelements, averaging may be required to process repeat spectra orreplicated sequences of illumination states, denoted as “replicates.”For example, an optical imaging system configured as in FIG. 69,includes a central detection fiber and concentric rings of NIRilluminators, R₁ through R_(K). Table 14 below provides the dimensionsand measurements of an embodiment corresponding to this configuration.

Let the state where an entire ring of illuminators of Ring 1,surrounding the detection element is turned on, be denoted as R1. In asimilar vein, {R1, R2, R3, ALL} represents a sequence where Ring 1, Ring2, Ring 3 and ALL Rings are turned on sequentially. A sequence {R1, R2,R3, ALL, R1, R2, R3, ALL} represents a “replicate” where the entiresequence {R1, R2, R3, ALL} is repeated. Another example of a replicatesequence is {R2, R3, R4, R1, ALL, R2, R3, R4, R1, ALL, R2, R3, R4, R1,ALL}, where a different sequence of illuminators is turned on andrepeated three times. Additionally, {R1, R1, R2, R2, R3, R3, ALL}represents a sequence where Rings R1, R2, and R3 are “repeats” but ALLis a singleton with no replicate. In the sequence {R1, R2, R3, ALL, R1,R2, R3, ALL}, M=4, and the number of replicates, denoted U, is equal to2. In the sequence {R2, R3, R4, R1, ALL, R2, R3, R4, R1, ALL, R2, R3,R4, R1, ALL}, M=5 and U=3.

Let the set of NRSEGs from all pairings of GL-p and NO-GL-q features bedenoted by {Δ{right arrow over (e)}_((p,q,R) _(t) ₎} where p=1, . . . ,P, and q=1, . . . , Q. To process repeats, NRSEG is computed for allpairings of GL and NO-GL features for each illumination state, R_(t),that is repeated. Say an illumination sequence presents up to U repeatsfor certain illumination states, where u≧1 and u=1, . . . , U. NRSEG forthe feature pair (p,q) is then {Δ{right arrow over (e)}_((p,q,R) _(t)_(,REP) _(u) ₎} for the repeat REPu associated with state t or the t-thillumination state including two or more rings (e.g., R2 and R4) for allp =1, . . . , P, and q=1, . . . , Q.

The set of U repeated NRSEG values from all pairings of GL-p and NO-GL-qfeatures are then averaged in some embodiments to yield sets {Δ{rightarrow over (e)}_((p,q, R) _(t) ₎} corresponding to all feature-pairs(p,q). As an example, the cardinality of the set {Δ{right arrow over(e)}_((p,q, R) _(t) ₎} corresponds to the number of distinct featurepairings as shown in FIG. 49, is 88, i.e., 22 times for eachillumination state R_(t) where M=4, and where the number of featurepairs, denoted Π, is 22. Each value in the set is averaged over thecorresponding U repeats, and the averaging of repeats for eachillumination state is performed prior to normalization of NRSEG for usein the Projection operation described below.

This {Δ{right arrow over (e)}_((p,q, R) _(t) ₎} set corresponds to theNRSEG for all features, averaged for all repeats, for all illuminationstates for the sample over the entire spectral bandwidth covered by theGL features. Monotonicity of the NRSEG values of each feature pairacross different illumination sets is tested, and feature pairs havingnon-monotonic NRSEG values are rejected in some embodiments. Theremaining feature pairs having monotonic NRSEG values acrossillumination states are generally called “acceptable” feature pairs.

Next, a weighting transform is applied in some embodiments to the NRSEGvalues y_(C) ^(i) for i=1, 2, . . . Π, to normalize all the featurepairs to provide an appropriate weighted contribution to the NRSEG,denoted “normalized NRSEG” for each concentration. Each normalized orweighted NRSEG appears as a data point by itself. From these, outliersmay be omitted and a mean of the weighted NRSEG values may be used infurther computations. Here, Π denotes the cardinality of the total setof feature pairs, the superscript i indicates the i-th feature pair, andsubscript C represents a particular analyte concentration in the set oftissue phantom concentrations, e.g., {0 mg/dl, 20 mg/dl, 40 mg/dl, . . ., 900 mg/dl}. Thus, C can be 40 mg/dl, 80 mg/dl, 180 mg/dl, etc.

The normalized NRSEG values y _(C) ^(i) may then be computed for all Πfeature pairs, or, alternatively, all of the acceptable feature pairs,as defined below, for each sample of the tissue phantoms using theproduct term given by:y _(C) ^(i) =y _(C) ^(i) *W(i _((p,q)))  (19)where W(i_((p,q))) is a numerical weighting coefficient, associated withan i^(th) feature pair i_((p,q)) where p and q represent the GL andNO-GL feature comprising the pair. The weighting coefficient for thefeature pair (p,q), i.e., W(i_((p,q))) is calculated using the purecomponent absorbance spectrum of the glucose analyte (as shown in FIG.28A) and the knowledge of spectral boundaries of the GL feature p andNO-GL feature q (as exemplified in FIG. 83). The product of y_(C) ^(i)and W(i_((p,q))) is defined as a “normalized feature pair.”

In the term

$\begin{matrix}{{AvgAbsorbance}_{(f)} = {\frac{1}{W}{\sum\limits_{l = 1}^{W}{{Absorbance}\left( {W\left( {f,l} \right)} \right)}}}} & (20)\end{matrix}$the variable W corresponds to the window width (number of distinctabsorbance values) of each feature, λ(f,l) is the lth wavenumber offeature, f, and Absorbance(W) is the absorbance of the pure componentspectrum at wavenumber W, and the integration is performed separatelyfor both the p and q features. Then,

$\begin{matrix}{{W\left( i_{({p,q})} \right)} = \frac{\max\limits_{u,v}\left( {{AvgAbsorbance}_{u}/{AvgAbsorbance}_{v}} \right)}{\left( {{AvgAbsorbance}_{p}/{AvgAbsorbance}_{q}} \right)}} & (21)\end{matrix}$such that a dimensionless quantity, max_(u,v)(AvgAbsorbance_(u)/AvgAbsorbance_(v)) is the maximum of the ratio of averageabsorbance of any GL feature u to its associated NO-GL feature v (overthe total feature-pair set as shown, e.g., in FIG. 49), computed usingthe glucose pure component spectrum shown in FIG. 28A. The terms,AvgAbsorbance_(p) and AvgAbsorbance_(q), which refer to the averageabsorbance of features p and q computed using the above definition ofAvgAbsorbance, can be used to compute the dimensionless number(AvgAbsorbance_(p)/AvgAbsorbance_(q)).

In summary, in various embodiments, the weighting coefficientW(i_((p,q))) may be used to scale all acceptable feature pairs from anyone illumination state to normalized feature pairs that have the correctnet contribution to the NRSEG corresponding to each glucoseconcentration. Weighting coefficients can also be defined using minimum,maximum, or median value of the absorbance over the region of interestof the pure component spectrum corresponding to the feature.

In one embodiment where the number of total available feature pairs=22,the number of illumination states is 4, and the number of computed NRSEG(un-weighted) is 88. These 88 values are used to determine monotonicityand slope in order to determine which feature pairs are acceptable. Theacceptable feature pairs are then weighted as discussed above andoutliers are removed that are more than two standard deviations awayfrom the mean.

As an example, if the number of acceptable feature pairs is 17, oneillumination state, e.g., R2, may be selected, and the respectiveweights may be applied to the 17 NRSEG values corresponding to R2, forthe acceptable 17 feature pairs, to obtain 17 normalized NRSEG values.From these 17 normalized NRSEG values, outliers (e.g., >2 times thestandard deviation away from the mean), may be removed. If the number ofoutliers removed is 3, the mean of the remaining 14 normalized NRSEGvalues may be used to determine two segments (or only one segment, ifthe corresponding analyte concentration is the lowest or highest), ofthe composite projector curve. It should be understood that thenumerical values described above are illustrative only, and that indifferent implementations, the numbers such as the total number offeature pairs, the number of acceptable feature pairs, the statisticalthreshold for outlier rejection, etc., can be different.

FIG. 71 shows one embodiment of the overall process of derivation of amapped projector curve set with NAG boundaries. Feature pairscorresponding to different, known concentrations of the analyte (e.g.,glucose) in a synthetic medium (e.g., tissue phantom) are obtained atstep 30. The concentration values can be adjusted according to anexpected dynamic range of the analyte in the media to be analyzed. Anembodiment of a collision computer, as described above, is used toobtain NRSEG values for each feature pair at step 40. An NRSEG-analyteconcentration curve is then generated at step 40 using the computedNRSEG values. At step 45, slopes of the curve are computed, and at step50 non-linearities in the slope, i.e., changes in the slope (also calleddiscontinuities), as described below, are determined. These changes inthe slope can be used to partition a single composite slope into anumber of intervals, each interval corresponding to individual slopesand projector curves. At step 55 the number of curves in a projectorcurve set is determined.

In some embodiments, the NRSEG-analyte concentration curve is generatedas a linear regression using a logarithm (base 10, base e, etc.) of theNRSEG values and the known or measured analyte (glucose) concentrationsin the set of tissue phantoms. The measurements can be obtained using areference measurement system such as an system that measures analyte(glucose) concentration in a sample. Thus, logs of the NRSEG values areregressed against the known/measured glucose concentration of tissuesamples. In determining the number of individual projector curves instep 55, in one embodiment piecewise computation of the slopes of theregression lines over samples separated by 10 mg/dl (or 5 mg/dl, 20mg/dl, 25 mg/dl, 40 mg/dl, etc.) sub-intervals over the entire range ofglucose concentrations of the tissue phantoms is performed. This entailsgeneration of linear regression coefficients between the logs of theNRSEG values and the known/measured glucose concentration of the tissuephantoms, as shown in FIG. 72. Steps in the generation andparameterization of all individual projector curves included in aprojector curve set are described with reference to FIG. 73.

As an example of piecewise computations of the regression slopes, theslope of a linear regression line between the logs of the NRSEGs fortissue phantoms with 20 mg/dl and 40 mg/dl glucose concentrations wascomputed from all samples with those concentrations and averaged overall the non-excluded replicates (described below), on a normalizedfeature by feature basis, as described below. The range of concentrationfrom 20 mg/dl to 40 mg/dl is one such piecewise sub-interval.

FIG. 72 illustrates this process. The log of the normalized NRSEG valuesfor several feature pairs (where the NRSEG value of a particular featurepair prior to normalization is based on an average of the correspondingNRSEG values over all replicates), measured for a tissue phantom with aglucose concentration of 20 mg/dl are shown plotted as points 50, andthe corresponding points for a tissue phantom with a glucoseconcentration of 40 mg/dl are shown as points 52. In general, there canbe up to Π (e.g., 22) times M (e.g., 4) normalized NRSEG values, whereall Π feature pairs are acceptable and each set of Π values correspondsto one of the M illumination states.

In the generation of a projector curve set, in some embodiments, onlyone set of up to Π normalized NRSEG values is used. For example, in oneembodiment, the illumination state R2, i.e., Ring_2, of theillumination/detection probe is selected, and the corresponding NRSEGvalues from the acceptable features pairs are normalized, as describedabove, in the generation of the projector curve set. Any feature pairswhose normalized NRSEG values are different according to a threshold(e.g., a deviation from the mean by more than one, two, three, etc.,standard deviations, a deviation from the mean by more than a thresholdspecified as an absolute limit or a percentage, etc.) (points 56) may beomitted from the regression calculation as outliers. A regression line54 is drawn through the mean of all remaining points at eachconcentration and becomes the piecewise sub-interval for the projectioncurve between 20 mg/dl and 40 mg/dl.

With reference to FIG. 73, in general, this process is repeated (steps10 through 35) for the normalized NRSEG computed using alltissue-phantom samples (“sample pairs”) at various concentrationsub-intervals, e.g., 10 mg/dl and 20 mg/dl, 40 mg/dl, 50 mg/dl, 50 mg/dland 60 mg/dl, and so on, up to the pair of samples between 800 mg/dl and900 mg/dl in the tissue phantom calibration dataset 30 in FIG. 71,wherein the sample pair sets may be arranged in order of increasingglucose concentrations. The piecewise sub-intervals used over the totalconcentration range may have different sub-interval ranges such as 10mg/dl, 15 mg/dl, 20 mg/dl, 40 mg/dl, etc. As several feature pairs maybe processed at each concentration, in some embodiments the normalizedNRSEG for each feature pair in a piecewise sub-interval is used as shownin FIG. 73. NRSEG values without normalization thereof may also be usedin some embodiments. The projector curve set is typically based on allof the feature pairs (FP) or all the acceptable feature pairs and allindividual projector curves.

In general, each tissue-phantom sample, except those tissue-phantomsamples at the lowest and highest concentrations, may be used togenerate two regression sub-intervals: (i) in the piecewise sub-intervalpreceding that concentration; and, (ii) the piecewise sub-intervalsucceeding that concentration. For example, if the sub-interval lengthis set to 10 mg/dl, the NRSEG for all features at the concentration of70 mg/dl would be used in the regression slope computation whenconsidering the piecewise sub-interval 60 mg/dl to 70 mg/dl, as well asthe sub-interval 70 mg/dl to 80 mg/dl. A linear regression slope foreach piecewise sub-interval, based on all feature pairs for thosesamples, is computed.

In various embodiments, a straight-line section of the compositeprojector curve in each sub-interval (e.g., the sub-interval [20 mg/dl,40 mg/dl]) is determined by plotting a linear regression line betweenthe log of all the non-omitted normalized (i.e., weighted) NRSEG valuesy ₂₀ ^(i) (for i=1, 2, 3 . . . , Π), for the tissue phantom with aglucose concentration of 20 mg/dl, and all the non-omitted, normalized(i.e., weighted) NRSEG values y ₄₀ ^(i) (for i=1, 2, 3 . . . , Π) for atissue phantom with a glucose concentration of 40 mg/dl. This process isillustrated with reference to FIG. 72, and was described above. Inparticular, for each concentration C (e.g., 20 mg/dl, 40 mg/dl, etc.),all Π (e.g., 22, in one embodiment) the log of the normalized NRSEGvalues are plotted, the outliers according to a threshold as describedabove are omitted, and the respective means of the remaining log valuesof the normalized NRSEG values is used to determine the correspondingregression lines.

With reference to FIG. 74, assume that at a glucose concentration of 20mg/dl, four feature pairs, FP₂₀ ¹, FP₂₀ ², FP₂₀ ³, and FP₂₀ ⁴ yieldnormalized NRSEG values y ₂₀ ¹, y ₂₀ ², y ₂₀ ³, and y ₂₀ ⁴. Also assumethat at glucose concentration of 40 mg/dl, four feature pairs, FP₄₀ ¹,FP₄₀ ², FP₄₀ ³, and FP₄₀ ⁴ provided normalized NRSEG values y ₄₀ ¹, y ₄₀², y ₄₀ ³, and y ₄₀ ⁴. Monotonicity requires that for at least onefeature pair, the NRSEG value prior to normalization, y ₄₀ ^(j) (forj=1, 2, 3, 4) be greater than the corresponding feature pair y ₂₀ ^(j)(for j=1, 2, 3, 4). It is necessary to ensure that the slope of eachsuch line is positive, that is that the normalized NRSEG y _(C) ^(i) ismonotonically increasing with glucose concentration. If monotonicity isnot confirmed, alternate feature pairs must be selected.

Table 10 below illustrates projector curve set generation in someembodiments where an NIR data collection subsystem has M illuminationstates R_(t)=1, 2, . . . , M. There are a total of Π feature pairsFP^(i), where i ranges from 1 through Π. For analyte concentration C_(k)corresponding to a particular tissue phantom, for each feature pairFP^(i), for each repeat of each illumination state Rt, an NRSEG value iscomputed using collision computing. For the analyte concentration C_(k),for each feature pair FP^(i), for each illumination state Rt, the NRSEGvalues computed for all repeats of R_(t) are averaged to obtain anaveraged NRSEG value y_(C) _(k) ^(i) ^(t) .

Monotonicity of y_(C) _(k) ^(i) ^(t) is tested across all illuminationstates R_(t), i.e., R₁ through R_(M) and, in some embodiments, onlythose features pairs that exhibit monotonicity are accepted for furtherprocessing. For all the accepted feature pairs, the averaged NRSEGvalues corresponding to any one illumination state (e.g., R₂, R₃,(R₂+R₄), etc.) are selected, and are represented as y_(C) _(k) ^(i).Each of these averaged NRSEG values corresponds to a particular acceptedfeature pair, and is weighted using a weight W(i(p, q)) associated withthe corresponding feature pair, to obtain a normalized NRSEG value y_(C) _(k) ^(i)=y_(C) _(k) ^(i)×W(i(p,q)). The computation of the weightis described above. The computation of y _(C) _(k) ^(i) is repeated fordifferent analyte concentrations Ck using different phantom tissuesamples.

TABLE 10 Illumination States R_(t) Feature Pairs FP^(i) R₁ R₂ . . .R_(M) i = 1 i = 2 y _(C) _(k) ² ² . y _(C) _(k) ^(i) ^(t) . . i = Π

Referring again to FIG. 73, the slopes of these piecewise linearregression lines (at step 40) correspond to sub-intervals of increasingglucose concentrations. The concentration sub-intervals chosen arenon-overlapping and do not have any gaps. If the concentration-samplepair set does not include samples separated by 10 mg/dl, then the nextlargest sub-interval available is used for computing the piecewiseregression slopes. For example, the sub-interval 100 mg/dl to 120 mg/dlwas used in one example, as no sample was prepared with 110 mg/dlconcentration. This generally ensures that there are no gaps between theregression curves corresponding to different concentration boundaries.

All the individual regression lines corresponding to different glucosesub-intervals over the entire range of concentration spanning 20 mg/dlto 900 mg/dl, as shown in FIG. 75, are then concatenated to form acontinuous, strictly increasing, single graph whose Y axis representsthe log of the mean of normalized NRSEG values after outlierelimination, due to NIR absorption by the analyte, and where the X axisrepresents the concentration of the analyte corresponding tosub-interval boundaries. This continuously increasing function iscomputed and shown in FIG. 76.

In various embodiments, a change in the value the slope of thecontinuous function constructed by concatenating the these linearregression lines over discrete piecewise sub-intervals, (an empiricallydetermined slope-change value that balances the need for smoothing ofindividual variations of slope against the number of intervals) istreated as a point of discontinuity in the NRSEG response to theconcentration of the analyte. The change in the value of the slope canbe specified as an absolute change or as percentage (e.g., 10%, 20%,50%, 60%, 100%, 150%, 200%, etc.) of the instantaneous slope. The pointsof slope change, where the change in slope is greater than 50%, of thecontinuous concatenated curve are shown in FIG. 76. The points of slopechange describe intervals of the composite curve, and the segments ofthe composite curve between a pair of consecutive points of change iscalled an individual projector curve. An individual projector curve maycorrespond to one or more sub-intervals.

In various embodiments, the continuous function, for all sub-intervalsof tissue phantom reference concentrations extending over the entireconcentration range, as shown in FIG. 76, is deconstructed intoindividual functions or curves where the first function extends from thelowest concentration to the concentration identified as the first slopediscontinuity. The second function extends from the concentrationassociated with the first slope discontinuity to the second slopediscontinuity, and so on, until the entire range is covered, asillustrated in step 40 of FIG. 73. The composite curve of NRSEG vs.concentration, incorporating the contribution of all feature pairs, ispartitioned into several individual projector curves, where eachindividual curve is identified by a change in the slope (as describedabove) from the previous curve. It is to be understood that any suitablethreshold value for a change in slope can be used to identify theboundaries of individual projector curves. For example, changes inlinear regression line slopes of greater than 5%, 10%, 20%, 60%, etc.,or an absolute difference in slope of greater than a specified thresholdcan be used to identify the boundaries of individual projector curves.

In general, if there are N_(a) distinct reference concentration values,there could be up to (N_(a)−1) concentration sub-intervals and,accordingly, there would be up to (N_(a)−1) regression line segments ofthe composite projector curve. The composite projector curve that is aconcatenation of the (N_(a)−1) segments can be partitioned into a set ofN_(g) individual projector curves, where N_(g)≦(N_(a)−1). A partitionboundary or a boundary of an individual projector curve, Γ_(P), can beidentified where the slope of an individual projector curve orregression line segment changes by more than a specified thresholdrelative to the slope of an adjacent individual projector curve orregression line segment. An individual projector curve, Γ_(P), mayinclude only a single regression line sub-interval corresponding to asingle concentration sub-interval (e.g., from 20 mg/dl up to 30 mg/dl,where the interval length is 10 mg/dl), or may include more than oneregression line sub-intervals. For example, a certain individualprojector curve may combine the regression line segments correspondingto the concentration intervals [60-70], [70-80], and [80-90] mg/dl intoa single interval [60-90]. In some embodiments, the slope of anindividual projector curve is determined by plotting a new regressionline that includes the log of the normalized NRSEG values for allfeature pairs obtained as sub-intervals that include 60, 70, 80, and 90mg/dl.

In general, the projector curve is an invertible, one-to-one function(i.e., the curve cannot be intersected at more than one point by avertical or horizontal line). Intersection by a vertical line at twodifferent points would mean that there are two different net energy gainvalues for the same concentration. Intersection by a horizontal line attwo different points would mean that for two different concentrationsthe net energy gain is the same. For a one-to-one mapping, neithercondition can be true.

FIG. 77 shows a “flipped” concatenated (also called composite) projectorcurve, where known analyte (glucose) concentration was the independentvariable (and is now plotted on the Y axis on the linear scale) and thelog of the normalized net, renormalized spectral energy gain was thedependent variable (and is now plotted on the X axis on a linear scale),as described below. With reference to FIG. 73, as the next step in theparameterization of the individual projector curves (step 50), the axesof the composite projector curve are reversed, such that the responsevariable or Y axis represents the analyte (glucose) concentration andthe logarithmic values of the normalized NRSEG is the explanatoryvariable represented on the X axis, to yield a “flipped projectorcurve,” as shown in FIG. 77. The log of the value of the averaged,normalized NRSEG values is also referred to as the log of the netanalyte signal (NAS) on the X axis of FIG. 77.

The overall processes of generating a flipped projector curve set thatis described above is summarized below in a pseudo-code form.

  Select any one illumination state (IS) (also called illuminationpattern) For each concentration value C_(k) {   For each feature pair i{      Compute NRSEG, averaged over all repeats of the selectedillumination      state, i.e., y^(i)      Compute normalized NRSEG, y^(i), by applying a weight W(i, (p, q)      corresponding to the featurepair   }   From all y ^(i) across all feature pairs, remove outliers  Compute mean of normalized NRSEGs of the remaining, i.e., acceptablefeature   pairs denoted Y_(C) _(k) . } For each analyte concentrationC_(k) in C₁ through C_(K-1) {   Draw a regression line segment joiningY_(C) _(k) and Y_(C) _(k+1) . Alternatively, generate a   regressionline segment using y_(C) _(k) ^(i) over all acceptable feature pairs,and y_(C) _(k+1) ^(i) over   all acceptable feature pairs. } Concatenateall regression line segments to obtain an composite projector curveDeconstruct the composite projector curve to obtain individual projectorcurves (i.e., the projector curve set Flip the composite projector curve

Measurement of Human Tissue for a Calibration Set

One or more calibration sets are generated to transform the net,renormalized spectral energy changes accumulated in the modified Zyotonwaveform to the analyte concentration. For example, in the case ofnon-invasive glucose measurement, calibration data are generated in twosteps, as described below.

In the first step, described above, a series of in-vitro experiments isperformed whereby different, known concentrations of the analyte ofinterest are added to tissue phantoms which are then spectrally imagedusing the same sensor hardware and illumination sequence that are usedfor analyzing glucose in human subjects. The spectra from these tissuephantom samples are processed by the collision computing process toensure that the resulting, computed spectral energy changes (e.g.,gains) are monotonically increasing or decreasing with an increase ordecrease in the concentration of the analyte. When monotonicity isachieved (by refinements of the components of the collision computingprocess, if necessary) a composite projector curve is generated betweenconcentration (as the independent variable) and spectral energy gain (asthe dependent variable), as described above.

In the second step, a series of paired measurements are made on one ormore human subjects, where tissue spectra are acquired along with pairedreference glucose values, which may be obtained using a conventionalinvasive technique requiring a blood sample. Two terms are used todescribe the accuracy of results in such an experiment: ARD and MARD.ARD, expressed as a percentage, is the “absolute relative difference” ofa single result from a reference value: ARD=|(referencevalue−experimental result)/reference value)|×100. MARD, also expressedas a percentage, is the mean of more than one absolute relativedifference values for either an individual or for multiple subjects:MARD=Average of all (|(reference value−experimental result)/referencevalue)|)×100. In general, the reference values can be obtained using asingle human subject or more than one (e.g., 2, 5, 9, 11, 15, etc.)human subjects.

In one embodiment that demonstrated glucose estimation accuracy with aMARD under 15%, such paired measurements are taken within one minute ofeach other, as glucose was found to be increasing or decreasing at ratesas high as 8 mg/dl per minute, as in the case of people with type 1diabetes who use insulin. Spectral energy gains due to glucoseabsorption in subjects' tissue using NIR diffuse reflectancemeasurements are then estimated using this collision-computingtechnique, at the same time the reference glucose measurement was alsotaken. The conditioning and collision computing processing for tissuespectra from human subjects is essentially the same as that used forprocessing spectral data from tissue phantoms. If monotonicity betweenreference glucose concentration and NRSEG is not achieved, thenprocessing of the data is further refined by modification of Zyotons,collision parameters, number of collisions, selection of frequencycomponents in the spectral energy computation, or changes to thecollision operator between collisions.

As described above, changes to the collision operator are achieved bymodifying a combination of one or more parameter that include thecollision grid bracket length (η), or the bracketed interaction operator({circle around (x)}), or revising the shift delay window (δ), or thephase operator (φ), or optionally the compression operator (ε), toadjust the length of the collision window. As described above, changesto the collision operator can be used to increase the tolerance of themeasurement to both coherent and non-coherent noise in the acquiredsensor data due to unpredictable changes to the medium, unpredictabledrift in the sensor (e.g., detector or illumination elements), and alsoto address changes in the confounder concentrations that impact SCR, andto address time-varying scatter losses. Changes in the collisionoperator can be made to avoid the need for additional data orreacquisition of a calibration dataset due to failure to achievemonotonicity between analyte reference concentration and the net,renormalized spectral energy changes obtained through collisioncomputing. One or more of the preceding collision operator parametersmay be revised to achieve a monotonic relationship of spectral energygain by the modified Zyoton over the glucose analyte concentrationrange. Once monotonicity has been achieved in the calibration datasetderived from human subjects, the spectral energy levels are projectedagainst, or recast in terms of energy absorption levels observed, asdescribed above, in the tissue phantoms with known glucoseconcentration, to derive a calibration set. The process is described indetail below.

In estimating tissue glucose concentration in human subjects, theaveraged (over repeats of respective illumination states) NRSEG for allfeatures, extracted from all replicate spectra for all illuminationstates is first computed as described below. Optionally, otherestimators such as L2 norm, median, and maximum likelihood (MLE) ratiocan be used instead of averaging. This averaged NRSEG is thentransformed into an estimated “glucose value” through the projectionprocess shown in FIG. 78. The projection process is a generalized methodand is applicable to determination of concentration of any analyte ofinterest such as urea, collagen, or lactate. For analytes that absorb indifferent NIR bands, different detectors or sources may be used.

Projection Process

Projection can be generally described as the process of representing theequivalence of the averaged NRSEG due to an analyte of interest (e.g.,glucose) in one measurement system (e.g., tomographic diffusereflectance spectroscopy) in one medium (e.g., human skin tissue) to theestimated, averaged NRSEG observed from another medium (e.g.,synthesized tissue phantoms created with different known levels of theanalyte), and imaged using the same sensor or instrument measurementsystem, in conjunction with the same processing (e.g., the same Zyotons,the same Zyoton collision operator, the same feature boundaries and thesame feature conditioning process, all of which are described above).

As shown in FIG. 78, using tissue spectra, the NRSEGs are computed forall feature pairs for all illumination states and are averaged over allrepeats of the respective illumination states on a feature pair byfeature pair basis. For each of the feature pairs for each sample foundto be acceptable as defined below, a Normalized Absorption Gradient(NAG) numerical value is computed (step 20) to select the appropriatemapped individual projector curve, from a set of several mappedindividual projectors curves included in a mapped projector curve set.In some embodiments, there may be only one individual mapped projectorcurve in the mapped projector curve set. Once the applicable mappedprojector curve is selected, it is used to transform the NRSEG into ananalyte concentration in step 30. The analyte concentration 40 can beoutput to the user, or further used in computation of clinical,diagnostic, screening, therapy effectiveness or regimen monitoring orwellness analytics; alarms provided to users, their care-team, friendsand family; population analytics; and longitudinal analysis. Details onprocesses for computing NAG, developing and using the mapped projectorcurve set (step 25) are described below.

In some embodiments, laboratory synthesized tissue phantoms in the formof liquid suspensions or gels serve as calibration systems forprojection. Projection, in general, is a two-step process: (i) The firststep includes the design and optimization of “mapped projector curves,”based on experimental data and samples, collected using bothtissue-phantom and human subjects, associated with known analyte (e.g.,glucose) concentrations, as described with reference to FIG. 71, and(ii) the second step includes the use of a mapped projector curve set,to transform the Normalized Absorption Gradient derived from theaveraged NRSEG in acceptable feature pairs, as estimated fromuncharacterized spectra (e.g., uncharacterized human tissue spectra)using the collision computing process, to determine the analyte levels.

The projector curves for analyte quantitation may be developed in adifferent medium than the uncharacterized media in which the analyte isto be detected and/or measured. The projector curves generally transforman information measure (the explanatory variable or averaged NRSEGgenerated through the collision computing process) to a responsevariable e.g., analyte concentration such as tissue glucoseconcentration expressed in mg/dl or mM/l). In estimating analyteconcentration in complex media, with high levels of interference fromconfounders with varying levels of absorption and scattering effects,more than one projector curve (denoted together as a “projector curveset”) may be used to cover the anticipated range of the responsevariable associated with the concentration of analyte of interest. Forexample, some embodiments for non-invasive glucose measurement use anine-member projector curve set.

As described above, the accuracy and precision of analyte concentrationestimation in unknown samples can be increased by designing the Zyotonsuch that the desired dynamic range of net, renormalized spectral energychanges can be measured, and that the Zyotons, along with properties ofother waveforms involved in the collision process, and the parameters ofthe collision operator, produce collisions that yield changes in thenet, renormalized spectral energy of the modified Zyoton that aremonotonic to analyte concentration levels, e.g., as described in step 60in FIG. 71, while analyzing human subjects in generating calibrationsets.

In the example of noninvasive glucose measurement, the NRSEG range isset to have a dynamic range of 8 to 10 orders of magnitude bycontrolling the collision count and parameters of the collisionoperator, while the actual range of glucose concentration seen in humantissue and blood generally extends over less than three orders ofmagnitude. Thus, Zyotons are designed to amplify small, linear changesin spectroscopic absorption due to changes in the analyte concentrationin the medium to large, logarithmic scale changes in the net,renormalized spectral energy gains. As a properly configured collisionoperator yields spectral energy gains that are monotonic to analyteconcentration, lower values of analyte concentration show smallerchanges in post-collision renormalized spectral energy and largeranalyte concentrations yield larger post-collision renormalized spectralenergies. Such nonlinear amplification generally results from varyinginelasticity of the collisions between Zyotons and conditioned spectralfeatures extracted from spectra of samples with varying analyteconcentrations.

The relationship between the net, renormalized spectral energy changesand varying analyte concentrations is typically not linear over therange of glucose concentrations seen in human tissue, thereby requiringthe using of several projector curves. Instead, this relationship, asshown below, is typically semi-linear, or linear in log-transformedspace. A relationship between a dependent and an independent variablecan be defined to be semi-linear if it includes the sum of a linear termand a low order nonlinear term. Semi-linear relationships may becomelinear when one or both of the variables are converted to logarithms orplotted on a graph with a logarithmic axis.

The mapped projector curve sets (also called projector curve sets) maybe developed for quantitation of any biochemical or chemical analyte ofinterest (and are not limited to the example glucose analyte) that arealso present in the tissue at the same time, and are of medical ortherapeutic value (e.g., non-invasively estimated collagen, urea,lactate, insulin, hemoglobin and other biochemical compounds). Insamples with several analytes of interest that absorb and scatter in thesame wavelength region accessible to the sensor, and where the differentanalytes of interest act as confounders against each other, differentconfigurations of the collision operator and different projector curvesets are generally required, with one set for each analyte. These may becalled multiplexed projector curve sets.

Typically, the projector curve sets are designed ahead of their use forprojection analysis, in a batch or an off-sequence mode as describedwith reference to FIG. 71. The operational use of the projector curveset may be batch-mode, off-sequence (for non-real-time applications) orin-line for real-time analysis. Off-line and in-line here refer toanalysis and processing of acquired-data at times that are differentfrom or concurrent with data acquisition times.

In some embodiments, referring to FIG. 71, the design-time calibrationstep and development of the projector curve set uses two experimentaldatasets in step 20: (a) a calibrated set of tissue phantoms that arecreated with known values of the analyte (e.g., glucose), and (b) a setof duplicate, paired reference measurements of blood glucose in humansubjects, obtained at step 10. For the first set, tissue phantoms with arange of glucose reference values used in one embodiment (as an input tothe projector curve set design process) included the followingconcentrations denoted as set C: 0 mg/dl, 20 mg/dl, 40 mg/dl, 50 mg/dl,60 mg/dl, 70 mg/dl, 80 mg/dl, 90 mg/dl, 100 mg/dl, 120 mg/dl, 150 mg/dl,200 mg/dl, 250 mg/dl, 300 mg/dl, 350 mg/dl, 400 mg/dl, 450 mg/dl, 500mg/dl, 600 mg/dl, 800 mg/dl and 900 mg/dl. Optionally, otherconcentrations than those listed above may be used. As the glucoseconcentration or the scattering properties of the synthetic tissuephantoms may change over time, a reference measurement of glucoseconcentration in the tissue phantom may be taken within a one minutetime window of imaging the tissue phantom.

The step 10 of FIG. 71 in one embodiment entails (a) acquisition of fiverepeated spectroscopic measurements (called “replicates”) taken at eachconcentration level (enumerated above), which includes the step ofmaking and breaking contact with the tissue phantom surface (in a gel orsolid phase phantom) or immersion and removal (if a stirred liquidIntralipid-based phantom was used); and, (b), duplicate, pairedreference measurements of blood glucose analyzed from an area on thedorsal side of the human subject's arm within two inches of where thespectroscopic human tissue data is acquired (or measurement of bloodglucose from the finger), for a group of individuals with differentlevels of blood glucose.

In generating some calibration datasets, the individuals includedsubjects with diabetes, those at risk of diabetes (such as withprediabetes), and, healthy subjects. Again, a maximum time lag of oneminute was generally maintained between the spectroscopic tissuemeasurement and an invasive glucose measurement with a reference method.To extend the range of glucose values in the calibration set, a modifiedOral Glucose Tolerance Test (OGTT) protocol and/or meal/exercisechallenge can be used in addition to daily-lifestyle measurements of thesubjects. All the preceding procedures were used to develop completedatasets for calibration purposes.

The calibration datasets having the two tissue-phantom and humanconstituent datasets described above, acquired ahead of operational-usetime, were analyzed using collision computing, in step 40 in FIG. 71(for tissue phantoms) and in step 60 (for human subjects), to develop amapped calibration curve set between NRSEGs, as computed from thespectral datasets, and the true value of glucose measured in the sampleusing a reference measurement system. In some embodiments, a projectorcurve set with boundaries of individual projector curves determined instep 55, as described above, that is derived from a tissue-phantomcalibration dataset, is denoted as Γ_(P).

Similarly, the calibration sets obtained using the averaged NRSEGs, ascomputed from a spectral dataset acquired from human skin tissue, andthe value of glucose measured in the subjects' tissue using a referencesystem such as a high-quality blood-glucose meter, is denoted Γ_(H). Invarious embodiments, in step 70, portions of the calibration sets areassociated with individual projector curves according to the analytesub-interval boundaries. For each portion of the calibration setsassociated with an individual projector curve, the NAG boundaries arecomputed at step 75, as described below. A projection or a mapping iscomputed at step 80, whereby each value over the entire range of Γ_(H)can be represented in terms of Γ_(P). This projector curve set is calleda mapped projector curve sent and is denoted as

as in. The construction of Γ_(P), Γ_(H) and

is described below. The cardinality of set Γ_(p) may range from 1through a maximum number Ξ (e.g., 5, 9, 12, 20, etc.) for an analytewith a dynamic range extending over a number of orders of magnitude.Also, the members of set Γ_(P)={(Γ_(P, 1)), (Γ_(P, 2)), . . . ,(Γ_(P, Ξ)),}, where Ξ is the number of individual projector curves in aprojector curve set.

In some embodiments, in the steps 40, 45, 60, and 65 of FIG. 71, anyfeature pairs that yield negative slopes or show a change of sign in theslope over the illumination states as shown in FIG. 79, are eliminatedfrom feature pair set from further consideration. If any of theprojector curves has all the feature pairs eliminated due to lack ofpositive slope, then all the feature pairs are considered suboptimal,and they are all rejected. Such a projector curve may then be labeled asNull, and the boundaries of the adjacent projector curves may beadjusted to subsume the entire concentration range of that nullifiedprojector curve. In some embodiments, an individual projector curve setto Null due to all the starting feature pairs failing the positive slopetest is considered differently from an individual projector curvesre-initialized to Null because there were no sample points acquired inthe concentration sub-interval associated with that individual projectorcurve.

FIGS. 80A and 80B show an example of the set of nine flipped individualprojector curves (Q1 through Q9 with associated NAG values) used in someembodiments for non-invasive glucose measurement. The curves in FIG. 80Aare nonlinear with the glucose range covered by each projector curve asshown on the composite projector curve in FIG. 77. In these flippedcurves, the glucose concentration is shown on the Y axis and the X axisshows normalized NRSEG value obtained from the Ring 2 illumination stateon a log scale. This example shows that the curves in the flippedprojector curve set can be overlapping. Such an overlap can result fromdifferent points of slope discontinuity when all the feature pairs takentogether do not meet the monotonicity condition described above. FIG. 81shows a single flipped projector curve covering a range of tissueglucose concentrations as a function of normalized net analyte signal(also called normalized NRSEG) estimated using collision computing.

Mapping of Human Tissue and Glucose Measurements to Projection Curves

Referring again to FIG. 71, the calibration sets obtained using theaverage NRSEG, as computed from a spectral dataset acquired from humanskin tissue, and the value of glucose measured in the subject's tissueusing a reference system, are denoted, as described above by Γ_(H). Onedifference between how the collision-computing results are obtained fromspectra generated using a synthetic medium (e.g., tissue phantom) andhow the collision-computing results are calculated for the calibrationdatasets. Unlike in a tissue phantom, the glucose concentration is onlyavailable at the time of measurement and cannot be controlled.Therefore, in various embodiments, the interval boundaries of theportions of calibration datasets are selected such that those boundariescan be matched with the interval boundaries of the projector curvedetermined from tissue phantom samples, as determined in step 55. Assuch, a particular interval of the calibration set, such as 100 mg/dl to120 mg/dl, may contain within it several net, renormalized spectralenergy gains of several concentrations between 100 mg/dl and 120 mg/dl,such as 101, 104, 107, 110, 112, 114, 117, and 119 and (all in mg/dl),in one example.

The NRSEG values in steps 40 and 60 (FIG. 71) are determined bycombining the net, renormalized spectral energy absorption from theentire dataset over several acceptable feature pairs. The spectralenergy absorption profiles are typically complex and non-uniform overthe concentration range, and cannot often be represented orparameterized in terms of a single linear regression curve. They areinstead represented using several projector curves, denoted by the termprojector curve set Γ_(P), as described above. In some embodiments forthe non-invasive estimation of glucose in human skin tissue, wherecalibration glucose levels may vary from 20 mg/dl to 900 mg/dl a, aprojector curve set with nine individual projector curves, as shown inFIG. 80B, is used to fully represent the relationship between: (a) theaveraged NRSEG, individually computed over different illumination statesover all acceptable feature pairs, and then combined to compute theNormalized Absorption Gradient (“NAG”); and (b) the glucoseconcentration.

Each analyte and non-analyte feature pair (e.g., GL and NO-GL featurepair) for each tissue spectrum is first examined to determine if it is“acceptable.” FIG. 79 shows curves called absorption gradients “AG”computed for five feature pairs FP1 . . . FP5 from a human spectroscopicsample. As an illustrative example, the four data points on the dashedline corresponding to FP3 represent the prior to normalization, i.e.,un-weighted NRSEG averaged over two repeats acquired using illuminationstates Ring 1, Ring 2, Ring 3 and All Rings. The specific values ofspectral energy gain are given in the table below the graph in FIG. 79.The absorption gradient computed for each feature pair, based on anillumination sequence using four illumination states as in this example,must be monotonically increasing over those four illumination states tobe determined to be an “acceptable” feature pair.

It is noted that the dashed line in the graph corresponding to featurepair FP3 does not have a monotonically increasing linear behavior overthe four illumination states as expected for this embodiment for thisfeature pair. It shows an increasing value of spectral energy gain withRing 2 compared to Ring 1, which then decreases for Ring 3, but againincreases for the ALL Rings illumination. This behavior is notconsistent with the model of glucose presence in human tissue, whereinterrogation of a thicker section of tissue would be expected to showmore absorbance due to glucose, and contravenes the response expectedusing tomographic imaging described above for non-invasive glucose,which is an increasing amount of glucose included within the photon pathmoving from Ring 1 to Ring 2 through Ring 3, with the greatest amount ofglucose in “all rings,” as those illuminations sequentially target theepidermis (Ring 1), the dermis (Ring 2), the subcutaneous through thedermis (Ring 3), and all three skin layers (All Rings).

Based on the above expected response, the feature pair FP3 in FIG. 79,is sub-optimal and the slope of the line is not usable to use incomputing a NAG for projection to select the appropriate projectorcurve, and the feature pair is not acceptable. In a similar vein, FP4and FP5 in FIG. 79 are not acceptable feature pairs as theirrenormalized spectral energy gain response also is different from whatis expected in tomographic imaging. On the other hand, the two solidlines corresponding to the renormalized spectral energy gains overdifferent illumination states using feature pairs FP1 and FP2 both havea positive slope, are monotonically increasing, and match the expectedbehavior of NIR absorption of glucose in the different layers of skin.FP1 and FP2 are thus both acceptable features, and the slopes of theirrespective regression lines are usable for the Projection process.Feature pairs meeting the monotonicity test are referred to as“acceptable feature pairs.”

It is to be understood that, in the context of calculating absorptiongradients and the Normalized Absorption Gradient, “monotonicity” forfeature pairs is assessed by regressing the NRSEG values for theillumination states in an illumination sequence against the distancebetween the source and detector, with the additional consideration herethat monotonicity is maintained when the illumination sequence includes,for example, two sequential illuminations using at least one ring withthe same separation distance, without a reversal in direction of themeasured energy. For example, duplicates of rings as in the illuminationsequence R1, R2, R2, R3, or when a following illumination state has atleast one ring with the same maximum separation distance as the previousillumination state, as in R1, R2, R3, ALL Rings, a feature pairexhibiting increasing or constant energy values across all theillumination states would be considered “monotonic” and thus“acceptable.” In these cases, when the duplicate measurements of energyfor the two R2 states in the first example, or the sequentialmeasurements of energy for the “R3, ALL Rings” pair of illuminationstates in the second example do not change direction, a feature pairwith these example illumination sequences and energy values woulddisplay a “monotonic” gradient, and the feature pair would be considered“acceptable.”

It is also to be understood that, if the illumination states wereconsidered in an opposite sequence, acceptable feature pairs could alsodisplay monotonically decreasing values, and still match the expectedabsorption behavior, thus becoming considered “acceptable featurepairs.” This example also clarifies the rationale for the selection andvalidation of feature pairs during design time, i.e., when the projectorcurves, calibration sets, and mapped projectors curves are generated.

The slope of the regression line, as determined above over the log ofthe NRSEG values for the four illumination states shown in FIG. 79, isdenoted the “absorption gradient” or “AG.” The determination of NAG,e.g., at step 40 (FIG. 82), for any sample entails two steps: Step 1 isthe computation of an absorption gradient, as above, for each acceptableanalyte and non-analyte feature pair (e.g., a GL and NO-GL feature pair)using the NRSEG averaged over one or more ring repeats for a sample (ifnecessary), and Step 2 is a normalization of the absorption gradientover all the feature pairs determined to be acceptable feature pairs (asdescribed below).

Referring to FIG. 82, the two steps in computation of the NAG are asfollows: In the first step, the absorption gradient computation, wherethe absorption gradient (AG) can be described as the slope of theregression line computed using the log of the numerical values of theNRSEG for all illumination states t=1, . . . , M over each acceptableanalyte and non-analyte feature pair (e.g., GL and NO-GL feature pair){p, q} where p=1, . . . , P, and q=1, . . . , Q, regressed against thetotal power of light delivered to the tissue in each illumination state,as measured with a light power meter with a detection range typicallycentered at 1550 nm.

TABLE 11 Typical Value of Total Light Power for Various IlluminationStates Illumination State Total Power @ 1550 nm Ring 1 1.00 Ring 2 1.50Ring 3 2.08 ALL Rings 4.58

The optional second step of the NAG computation involves normalizationof the absorption gradients (AGs), as computed above, across all theacceptable feature pairs associated with a sample including all spectraacquired during an illumination sequence and their replicates. LetAG(t_(p,q)) denote the computed AG of the t^(th) acceptable feature pairin Step 40 of FIG. 82, in the first step of NAG computation. In thesecond step the separate AG values are normalized and averaged over allAG(t_(p,q)) for all N_(t) acceptable feature pairs, by taking theaverage of the product term given by:

$\begin{matrix}{\overset{\_}{NAG} = {\frac{1}{Nt}\left( {\sum\limits_{1}^{t}{{{AG}\left( t_{p,q} \right)}*{W\left( {p,q} \right)}}} \right)}} & (22)\end{matrix}$where the result NAG is the Averaged Normalized Absorption Gradient forthe sample; with AG(t_(p,q)), is as defined above, i.e., the absorptiongradient of the t^(th) acceptable feature pair (p,q) associated with asample, combining results from several illuminations of an illuminationsequence; and W(p, q) is a numerical weighting coefficient associatedwith an acceptable feature pair (p,q) where p and q represent theanalyte (e.g., GL) and non analyte (e.g., NO-GL) features, respectively.The weighting coefficient for the feature pair (p,q), i.e., W(p,q) iscalculated as defined above, using pure component absorbance spectra ofglucose (as shown in FIG. 28A) and the knowledge of spectral boundariesof the analyte feature p and non-analyte feature q. An example of GL andNO-GL features is shown in FIG. 83.

In various embodiments,

${AvgAbsorbance}_{(f)} = {\frac{1}{W}{\sum\limits_{l = 1}^{W}\left( {Absorbance}_{(l)} \right)}}$where the average absorbance AvgAbsorbance_((f)), for a feature f, witha feature length of W, in wave numbers, is the average of l purecomponent absorbance values (scaled to any absorbance unit), at eachdiscrete wavenumber position contained in the feature, such that W isthe product of l and resolution of the sensors (in wavenumbers). Thus:

$\begin{matrix}{{W\left( {p,q} \right)} = \frac{\max\limits_{u,v}\left( {{AvgAbsorbance}_{u}/{AvgAbsorbance}_{v}} \right)}{\left( {{AvgAbsorbance}_{p}/{AvgAbsorbance}_{q}} \right)}} & (23)\end{matrix}$such that a dimensionless quantity, max_(u,v) (Avg Absorbance_(u)/AvgAbsorbance_(v)) is the maximum of the ratio of average absorbance of anyanalyte (e.g., GL) feature u to its associated non analyte (e.g., NO-GL)feature v over the total feature set, such as that shown in FIG. 83,computed using the pure component spectrum. An example of the purecomponent spectrum for glucose is shown in FIG. 28A. The values,AvgAbsorbance_(p) and AvgAbsorbance_(q), which generally refer to theaverage absorbance of features p and q computed using the abovedefinition of AvgAbsorbance, are used to compute the dimensionlessnumber (AvgAbsorbance_(p)/AvgAbsorbance_(q)).

In summary, the weighting coefficient W is used to scale all featurepairs to have the same net contribution for the purpose of projectingthe NRSEG to analyte quantity or concentration, averaged over allreplicate illumination sequences in a tomographic acquisition. Once theNormalized Absorption Gradient values have been computed for allacceptable feature pairs and averaged to obtain NAG, this value is usedis various embodiments in selection of the applicable projector curveand in the determination of the analyte concentration at step 10 (FIG.78).

Referring again to FIG. 71, steps 65 through 80 show how the projectorcurve set mapping, represented as

:Γ_(H)→Γ_(P), is established using data from both human and tissuephantom datasets. The human calibration dataset (including NRSEGsderived from several pairs of tissue spectra and their associated bloodglucose reference values), is partitioned into subsets (referred to as“projection sets”), such that paired data are separated on the basis oftheir reference values into the same glucose intervals as used for thetissue-phantom dataset, i.e., the intervals defining the individualprojector curve set Γ_(P) boundaries.

The processing of NRSEGs for different illumination states obtainedusing collision computing, associated with the feature pairs in theprojection sets constructed using a human dataset is typically differentfrom those in the tissue-phantom dataset. The NAG values are computed,as described above, in generating the projection sets, which are groupsaccording to the concentration values measured using a reference system,and associated with concentration value boundaries of individualprojector curves. A different net energy gain is expected due to anexpected increase in pathlength in the phantoms. Specifically, (i) asthe tissue phantoms used are one-layered system, no NAG is computed forthe NRSEG obtained using tissue phantoms for the feature pairs whendifferent rings are illuminated. However, a check is made for:

$\begin{matrix}{{\Delta\; e_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{1}})}} < {\Delta\; e_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{2}})}} < {\Delta\; e_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{3}})}} < {\Delta\; e_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{ALL}})}}} & (24)\end{matrix}$for all feature pairs (p,q). This check is due to an increase inpathlength through the glucose-containing phantom successively in rings1, 2, 3 and ALL.

Also, the slope of the linear regression line obtained using the logvalues for

Δ e_((GL_(F_(p)), NO − GL_(F_(q)), Z_(r), R₁)), Δ e_((GL_(F_(p)), NO − GL_(F_(q)), Z_(r), R₂)),       Δ e_((GL_(F_(p)), NO − GL_(F_(q)), Z_(r), R₃)),  and  Δ e_((GL_(F_(p)), NO − GL_(F_(q)), Z_(r), R_(ALL))), regressed against the illumination states R1, R1, R3, ALL Rings, mustgenerally be positive (or negative, if the illumination sequence is suchthat the successive illumination states correspond to decreasing depthof photon paths under the skin). NRSEG monotonicity as specific byrelationship in Equation (24) may be required in various embodimentshaving several illumination rings and states, e.g. R₁, R₂, R₃, . . . ,R_(i), R_(i+1), . . . R_(T), ALL where T>1 and the ring indices 1, 2, .. . , i, i+1, . . . , T, ALL are sorted by total power delivered to theskin by individual ring. If this slope condition is not met, the featurepair is not an acceptable feature pair, and it may be eliminated fromnormalization calculations and/or another feature pair may be selected.

In one embodiment, the paired data of tissue spectra and theircorresponding glucose concentration reference values in the humancalibration dataset, are arranged according to the same intervalboundaries as computed in steps 50 and 55 in the process described withreference to FIG. 71, and grouped into nine or fewer projection sets,depending on the range of reference glucose values. Typically, no slopediscontinuity check computations are performed as in the case of datafrom tissue phantoms.

Based on the grouping results, some individual projector curves may notbe associated with any data points (i.e., they are empty and may belabeled as “Null”). This implies that no human calibration data wereobtained for such intervals. The Null labeled projectors curves may bediscarded from further consideration similarly as projections setslabeled as Null may be discarded (in step 30 FIG. 82), as describedabove. The boundaries of the adjacent individual projector curves maythen be adjusted to subsume the discarded individual projector curve.

The process for generating the mapping

:Γ_(H)→Γ_(P) in some embodiments is shown in FIG. 82. This processtypically uses the NAG values, and generally maps the NRSEG, which canalso be denoted as the normalized net analyte signal (NAS), from humannon-invasive calibration measurements to estimate glucose levels foruncharacterized subjects. Once the projector curve set (Γ_(P)) has beenparameterized (step 50 of the process shown in FIG. 73), the mapping

development can be completed using the process flow starting at 5 asshown in FIG. 82.

In some embodiments, calibration sets including the NRSEG data, i.e.,gain

${\Delta\;{\overset{\rightarrow}{e}}_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}}\mspace{385mu}$for all t=1, . . . , M for each analyte (e.g., GL) and non-analyte(e.g., NO-GL) feature pair {p, q} where p=1, . . . , P, and q=1, . . . ,Q, are obtained at step 15 (FIG. 82). The human calibration dataset ispartitioned into subsets (called projection sets) corresponding to theprojector curves, where analyte-concentration boundaries of the subset(i.e., each projection set) are the same as the analyte-concentrationboundaries of the projector curves. Also, one or more projection setscan be Null, as described above, i.e., human data may not be availablefor any concentration within the boundaries of that particular projectorcurve (e.g., 0-20 mg/dl, 640-700 mg/dl). In concentration regions suchas these, where human data are not available, a correction factor, basedon the values obtained for NAG using the nearest available concentrationregions for which human data are available, may be used to extrapolatethe tissue-phantom spectral data to provide NAG values for theseregions. A check for monotonicity in the NRSEG as a function ofreference glucose concentration may be made for human samples over thetotal range of analyte (e.g., glucose) concentrations collected, inorder to validate the selection of feature pairs and selection of thecollision computing parameters. For example, the NRSEG for aconcentration of 125 mg/dl must be greater than that for 101 mg/dl inthe human calibration dataset.

The absorption gradient obtained by regressing NRSEG (on a log scale orany other numerical scale that can linearize the regressionrelationship) against signal power delivered to the medium, thesource-detector distance, or the reciprocal of either, where the NRSEGvalues are obtained using collision-computing or via estimation ofabsorption due to analyte using another computation technique, is usedto select a suitable projector curve, as described below. The NAG canaccount for variations in the uncharacterized media to be analyzed, suchas variation in skin properties of one person to another and, as such,allows for the selection of a projector curve that corresponds to theproperties of the medium to be analyzed without having to calibrate thatparticular medium. The use of the NAG thus facilitates universalcalibration, i.e., calibration that does not depend on the particularmedium to be analyzed.

Radiation/detection systems having several detection elements and asingle source, or several illumination elements and a single detector,or several radiation sources and several detection elements can be usedin computing the NAG. The use of AG or NAG in transforming acquired datato an analyte concentration is a robust mechanism to obtain analyteconcentrations in a medium with high levels of interference fromconfounders. For systems implementing spectroscopic tomography, use ofAG and NAG provides a robust mechanism for also determining if theunderlying measurement hardware is functioning properly. A null AGvalue, over time, as seen in several samples can indicate a systemmalfunction. In various embodiments, AG or NAG can be used in bothin-vitro and in-vivo analysis of uncharacterized samples that arespectroscopically imaged using one or more radiation sources and one ormore detectors.

Referring back to FIG. 82, for each projection set that is not labeledas Null, a check is made at step 30 to ensure that there is at least oneacceptable feature pair (pairing of analyte (e.g., GL) and non-analyte(e.g., NO-GL) features as described above. The NAG is a weighted averageof AGs across acceptable feature pairs. Any Null projection set withinΓ_(H), and any projection set without at least one acceptable featurepair yielding a positive AG value, are discarded from any furtherprocessing at step 30. The NAG computed using the normalized, averagedAG values from all acceptable feature pairs associated with all pairedsample members of Γ_(H), are used to compute a range at step 50 asΓ_(H){φ_(i)}<φ_(iL), φ_(iU)> where Γ_(H){φ_(i)} represents the i^(th)member of the set Γ_(H), and φ_(iL) and φ_(iU) represent the lowest andhighest value of the NAG for the interval, over all acceptable featurepairs associated with all samples in the interval. As indicated by theflow loops 42 and 52, this computation is repeated for all the sampleswith all acceptable feature pairs for all the groups in Γ_(H). Thisprocess is further illustrated with reference to FIGS. 84A and 84Bbelow. The NAG values thus relate the NRSEG values or the logs thereoffor a projection set in Γ_(H) to its associated member in set Γ_(P)through a mapping process.

With reference to FIG. 84A, a portion of the composite projector curveis partitioned into two individual projector curves S₁ and S₂. Theanalyte concentration boundaries of S₁ and S₂ are [g1, g2] and [g2, g3],respectively. The values g1, g2, and g'can be obtained from a selectionof the tissue phantom samples. In one example, where the analyte isglucose, these boundaries can be [80, 110], [110, 130], all in mg/dl. Itis to be understood that a composite projector curve may be partitionedinto more than two, e.g., 5, 6, 9, 10, 12, 15, etc., individualprojector curves.

The NAG values are computed from calculation of NRSEG corresponding toanalyte concentrations in human tissue spectra. During calibration, theanalyte concentrations are measured using an invasive reference method.In one example, let the analyte concentration values for which NAG valuewere computed be: g₁ ^(r), g₂ ^(r), g₃ ^(r), g₄ ^(r), g₅ ^(r), g₆ ^(r),g₇ ^(r), and g₈ ^(r), the superscript “r” indicating that theseconcentration values were obtained using a reference method. After theseconcentrations and the corresponding NAG values are determined, it isfurther determined that g₁ ^(r), g₂ ^(r), g₃ ^(r), and g₄ ^(r) areincluded in the range [g1, g2] and g₅ ^(r), g₆ ^(r), g₇ ^(r), and g₈^(r) are included in the range [g2, g3]. Therefore, the concentrationvalues g₁ ^(r), g₂ ^(r), g₃ ^(r), and g₄ ^(r) and the corresponding NAGvalues are associated with S₁, and the concentration values g₅ ^(r), g₆^(r), g₇ ^(r), and g₈ ^(r) and the corresponding NAG values areassociated with S₂. It should be understood that fewer or more thanfour, and/or different numbers of value pairs can be associated withdifferent individual projector curves S_(i). In one example where theanalyte is glucose, g₁ ^(r), g₂ ^(r), g₃ ^(r), and g₄ ^(r) are 83, 87,94, and 106, respectively, and g₅ ^(r), g₆ ^(r), g₇ ^(r), and g₈ ^(r)are 112, 116, 121, and 128, respectively.

In some embodiments, the computed NAG is within the lower and upperbound NAG values if the computed NAG is equal to or greater than thelower bound NAG value and is equal to or less than the upper bound NAGvalue. In some embodiments, the computed NAG is within the lower andupper bound NAG values if: (i) the computed NAG is greater than thelower bound NAG value and is equal to or less than the upper bound NAGvalue; or (ii) the computed NAG is equal to or greater than the lowerbound NAG value and is less than the upper bound NAG value; or (iii) thecomputed NAG is greater than the lower bound NAG value and is less thanthe upper bound NAG value.

With reference to Table 12 below, consider an interval [110, 130] of oneexample of a composite projector curve S. An individual projector curveS₄≡S_([110-130]) is associated with this interval. Assume that acomplete set of feature pairs includes five feature pairs, namely, FP1,FP2, FP3, FP4, and FP5. It is to be understood that in general, therecan be fewer than five or more than five (e.g., 10, 20, 30, 50, etc.)feature pairs that can be considered for the analysis described herein.Assume further that for the selected interval [110, 130], threereference concentration values, namely, 112, 121, 126, were obtainedusing a reference invasive method. Here again, it is to be understoodthat these values are illustrative only in that different referencevalues and different numbers of reference values, e.g., 1, 2, 4, 6, 10,etc., may be obtained within a selected interval. For each referenceconcentration value, for each available feature pair, the monotonicityis tested as described above.

In addition, unlike the embodiment described above, where monotonicityis tracked only over adjacent ring illumination states, it would bepossible to utilize varying illumination states for certain samples withparticular features or tissue layer thicknesses, and an embodiment couldbe constructed with a probe having 6 illumination (or detector) rings.For example, the same glucose concentration, data from person A may showmonotonicity across rings 2-3-4 while data for person B may showmonotonicity across rings 3-4-5-6. Thus using either the same featuresor different features, the projection system could test monotonicitywhile rejecting data from rings 1, 5, and 6 for person A, and from rings1 and 2 for person B.

TABLE 12 Concentration 112 121 126 FP1 × × AG₁₂₆ ¹ FP2 AG₁₁₂ ² AG₁₂₁ ² ×FP3 AG₁₁₂ ³ × AG₁₂₆ ³ FP4 × × × FP5 AG₁₁₂ ⁵ × × NAG NAG ₁₁₂ = NAG ₁₁₂ =NAG ₁₂₆ = ⅓(W₂AG₁₁₂ ² + (W₂AG₁₂₁ ²) ½(W₁AG₁₂₆ ¹ + W₃AG₁₁₂ ³ + W₃AG₁₂₆ ³)W₅AG₁₁₂ ⁵)

As illustrated in Table 12 above, for the reference glucoseconcentration value 112, three of the five feature pairs are accepted;for the reference glucose concentration value 121, only one feature pairis accepted; and for the reference glucose concentration value 126 twofeature pairs are accepted. For the accepted feature pairs, respectiveabsorption gradients AG_(C) _(k) _(r) ^(i) are computed, where thesubscript C_(k) ^(r) represents the corresponding reference analyteconcentration, and the superscript i indicates the correspondingacceptable feature pair. For each reference analyte concentration C_(k)^(r), the absorption gradient(s) of the acceptable feature pairs areweighted using the weights computed as described above, and theseweighted absorption gradients are averaged to obtain a normalizedabsorption gradient NAG _(C) _(k) _(r) . In the table above, the weightW_(i) represents the weight W(i(p,q) described above.

The individual projector curve S₄ is associated with the minimum andmaximum of all NAG _(C) _(k) _(r) values, where all reference analyteconcentration values C_(k) ^(r) are associated with the individualprojector curve S₄, as: φ_(4L)=min(NAG ₁₁₂,NAG ₁₂₁,NAG ₁₂₆); andφ_(4U)=max(NAG ₁₁₂,NAG ₁₂₁,NAG ₁₂₆). This subprocess is repeated foreach individual projector curve. The overall processes of generating aprojection set that is described above is summarized below in apseudo-code form.

Similarly, the rings used in a specific embodiment to calculate NAG andNRSEG will depend upon the selected wavelength range. For example, in a6-ring system, in the region above 1500 nm, only the first four ringsmay be used for the computation of NAG, with the combined energy gainfrom rings 2 and 3 being used for glucose prediction. Below 1350 nm, allsix rings may be used to compute NAG and the mapping from NRSEG toglucose is based upon rings 2-4, 3-5 or 2-5 depending upon theembodiment.

This process is described in the pseudo-code below:

For each individual in a group of individuals {    Perform an analyte(e.g., glucose) measurement (e.g., determination of analyte   concentration) using a reference method    Perform a correspondingcollision computing (CC) measurement, where the CC    measurement isassociated one or more analyte-non-analyte feature pairs, and to perform   the CC measurement, for each feature pair {       Obtain up to MNRSEG values, where M is the number of unique illumination       states(IS) such as (I₁, I₂, . . . , I_(M)), e.g. (R2, R3, R4, ALL), in anillumination       sequence          // Each NRSEG value is associatedwith a respective, particular          // illumination pattern (e.g.,R4), and can be an average of NRSEG          // values across therepeats of that particular illumination pattern       Test monotonicityof the M NRSEG values across the M IS (ordered by the    amount of powerdelivered to the sample)       Accept only those feature pairs thatsatisfy the monotonicity condition    }    For each accepted featurepair {       Compute absorption gradient (AG) using the corresponding MNRSEG values    }    Compute NAG as a weighted average of AGs of allaccepted feature pairs, normalized by the weighting coefficientsestablished on basis of the relative absorbances of the individualfeatures for pure component spectra for the analyte } Repeat for theselected individual, the above iteration at a different time to obtain adifferent reference analyte measurement and a corresponding different CCmeasurement, and a different NAG associated therewith } // At the end ofthis sub-process, several reference analyte measurements and //corresponding NAG values would be obtained Sort the pairs <ref_analyte_measurement, NAG> by analyte measurement values For eachindividual projector curve S_(i) {    Associate one or more pairs toS_(i) according to the analyte measurement boundaries of S_(i).    Theassociation can be represented as:       S, (g_(L), g_(U)) <==>Projection_Set_i [<g'_(L), NAG>, . . . , <g'_(U), NAG>],       whereg_(L) ≦ g'_(L) and g_(U) ≧ g'_(U).    Associate min (Projection_Set_i(NAG)) and max (Projection_Set_i (NAG)) with S_(i). }

Use of Projection Curves to Determine Glucose in Noninvasive Samples

For each flipped, individual Projector Curve respectively, the variablesslope_(i) and y-intercept_(i) denote the slope and y-intercept of thelinearized i^(th) individual projector curve with analyte (e.g. glucose)concentration on the Y axis and the log values of NRSEG on the X axis,as shown in FIG. 80B. Thus, in general, a mapping

:Γ_(H)→Γ_(P) can be represented as

:{{Γ_(H){φ₁}<φ_(1L),φ_(1U) >→S ₁ {<g _(1L) ,g _(1U)>,slope₁,y-intercept₁}},{{Γ_(H){φ₂}<φ_(2L),φ_(2U) >→S ₂ {<g _(2L) ,g _(2U)>,slope₂,y-intercept₂}},. . . ,{{Γ_(H){φ₉}<φ_(9L),φ_(9U) >}→S ₉ {<g _(9L) ,g _(9U)>,slope₉,y-intercept₉}}}where the variables in the set notation are as described above, with thevariable i being set to 1, 2, . . . , 9, in one embodiment. This

is a set of mappings to project NRSEG values from human subject tissueto analyte concentration values in tissue phantoms, and is used forselecting the appropriate mapped individual projector curve, from a setof mapped individual projector curve as shown in FIGS. 80A and 80B,prior to calculating the analyte concentration for a subject.

In some embodiments for noninvasive glucose measurement, the NAG valuesfor the nine mapped individual projector curves range from a curve withNAG values of approximately 0.001 to about 11.23, as shown in FIG. 80A,from a first curve with a NAG range of 0.001 to 0.052 covering theglucose range 0 mg/dl to about 20 mg/dl, to the ninth curve with a NAGrange of 7.11 to 11.23 covering glucose concentrations from about 450mg/dl to 700 mg/dl.

In various embodiments, the mapped individual projector curves

are denoted as {φ₁, . . . , φ₉}. Each curve, φ_(i)ε

, spans a range associated with analyte concentration ranging between alower limit GL_(il) and an upper limit GL_(iU). Furthermore, each of themapped individual projector curves, represented by φ_(i) is associatedwith a NAG range given by {<φ_(iL), φ_(iU)> where i=1, . . . , 9} andhas the attribute of a range of NAG values with a <lower,upper> valuepair, as described above, and as listed, e.g., in Tables 12 and 13.Thus, for a curve Si, let the coordinates of the start pair be (g_(iL),e_(iL)) and the end pair be (g_(iU), e_(iU)), where g represents theanalyte concentration obtained via a reference method, and e representsthe logarithm of the corresponding normalized, averaged NRSEG due toabsorption by the analyte in a tissue phantom, as determined bycollision computing.

TABLE 13 Glucose Glucose Slope of Intercept Curve Range Range Si (on logof Si (on NAG NAG Si (low) (upper) scale) log scale) (Φ_(iL)) (Φ_(iU)) 11 20 12.015 −5.12E−05 0.0001 0.052 2 15 60  3.6115  2.708 0.053 0.12 350 80  0.7522  3.912 0.121 0.36 4 70 130  0.68763  4.2484 0.361 0.60 5120 180  0.36595  4.7865 0.610 0.96 6 180 250  0.26772  5.1909 0.9612.40 7 220 400  0.36208  5.3889 2.41 4.70 8 350 500  0.51773  5.81014.71 7.10 9 450 700  1.6182  5.7618 7.11 11.23

As shown, in FIG. 80A, each of the example NAG curves generally displaysa nonlinear relationship between NRSEG and glucose concentration. Thesemapped individual projector curves are semi-linear, and theirlog-transformed relationship (i.e., the log of the NRSEG values againstthe corresponding glucose reference values), is generally linear overthe interval <g_(iL),g_(iU)> with slope_(i) and y-intercept_(i). Thelinearized curves corresponding to the curves shown in FIG. 80A areshown in FIG. 80B. In some embodiments, the linearized Projector curvesin FIG. 80B, with reference glucose concentration plotted on the logscale on Y axis and the log of Ring_2_Egain* (or normalized NRSEG fromRing 2) plotted on the X axis are used in the overall projection processto estimate glucose concentration values.

In various embodiments, in addition to the (g_(iL), e_(iL)) and (g_(iU),e_(iU)) pairs, there is a min and max NAG value associated with eachφ_(i). This means that NAG values mapping to each curve S_(i) will varyin a range [φ_(i) ^(min), φ_(i) ^(max)]. The slope of the mappedindividual projector S_(i) maps the log of NRSEG to analyteconcentration. The intervals [φ_(i) ^(min), φ_(i) ^(max)] are set bycomputing AG over all N_(t) acceptable feature pairs for eachcalibration subject tissue sample, and are associated with analyteconcentration data points that fall within the boundaries of S_(i).Thus, in various embodiments [φ_(i) ^(min), φ_(i) ^(max)] are theminimum and maximum NAG values for the projection set associated with anindividual projector curve. For example, if S_(K) ranges from 70 mg/dLto 100 mg/dL, the data points 72, 75, 83, 90, and 96 mg/dL wouldcorrespond to S_(K). Then φ_(i) ^(min) would correspond to the NAG valueassociated with the data point with a glucose concentration of 72 mg/dLand φ_(i) ^(max) would correspond to the NAG value associated with thedata point with a glucose concentration of 96 mg/dl, and the Curve S_(K)is extrapolated to cover glucose concentrations as low as 70 mg/dl or ashigh as 100 mg/dl, i.e., to the boundaries of the adjacent curves, e.g.,the boundaries of the curves S_(K−1) and S_(K+1).

In general, this range results from subject-to-subject tissue morphologyand physiology differences, sampling variability, and sensor drift inmultiple samples. This means that the estimated NAG value used to mapthe log of the NRSEG on to any curve Si can vary in a range [φ_(i)^(min), φ_(i) ^(max)], also denoted [φ_(iL), φ_(iU)] to allow forsampling, experimental and other variabilities described above.

Referring again to FIG. 84A, without the loss of generality, g₁ ^(r),<g₂^(r)<g₃ ^(r)<g₄ ^(r)<g₅ ^(r)<g₆ ^(r)<g₇ ^(r)<g₈ ^(r). Therefore,concentration boundaries [g_(1L)=g₁, g_(1U)=g₂] and [g_(2L)=g₂,g_(2U)=g₃] are associated with the individual projector curves S₁ andS₂, respectively. The map

, Γ_(H){φ₁} can be specified as <φ_(1L), φ_(1U)>, and the map

Γ_(H){φ₂} can be specified as <φ_(2L), φ_(2U)>. The NAGs correspondingto the reference analyte concentrations [g₁ ^(r), g₂ ^(r), g₃ ^(r), g₄^(r)] are associated with the individual projector curve S₁, and aredenoted [NAG ₁ ¹, NAG ₂ ¹, NAG ₃ ¹, NAG ₄ ¹]. Similarly, the NAGscorresponding to the reference analyte concentrations [g₅ ^(r), g₆ ^(r),g₇ ^(r), g₈ ^(r)] are associated with the individual projector curve S₂,and are denoted [NAG ₁ ², NAG ₂ ², NAG ₃ ², NAG ₄ ²]. In this notation,(NAG _(k) ^(i), in general), NAG represents the normalized absorptiongradient computed as described above, the superscript “i” indicates theparticular individual projector curve with which the NAG is associated,and the subscript “k” indicates an analyte concentration, determinedusing the reference system, belonging to a member of the projection setcorresponding to the i-th individual projector curve. As such, in thetwo example of maps described above, φ_(1L)=min(NAG ₁ ¹, NAG ₂ ¹, NAG ₃¹, NAG ₄ ¹) and φ_(1U)=max(NAG ₁ ¹, NAG ₂ ¹, NAG ₃ ¹, NAG ₄ ¹).Similarly, φ_(2L)=min(NAG ₁ ², NAG ₂ ², NAG ₃ ², NAG ₄ ²) andφ_(2U)=max(NAG ₁ ², NAG ₂ ², NAG ₃ ², NAG ₄ ²).

It is to be understood that in some embodiments, only a singleindividual projection curve is generated from synthetic calibrationsamples, calibration subjects, and corresponding glucose value ranges.In these embodiments, the analyte concentration can be determined usingthe average of the normalized NRSEG values corresponding to allacceptable feature pairs corresponding to one particular illuminationstate. This average NRSEG value can be mapped directly to the analyteconcentration using the available projector curve, and the NAG need notbe used to select a projector curve as only one curve is available.Optionally, the NAG value may nevertheless be computed in suchembodiments to test monotonicity across different illumination states.

EXAMPLE OF A CALCULATED GLUCOSE RESULT

In some embodiments for non-invasive glucose measurement, the abovecalculated average NRSEG for each illumination state of an illuminationsequence describes a point. When three single-ring illumination statesare used, three NRSEG values are generated for all feature pairs, oneassociated with each illumination state. In another embodiment, wherethere are six illuminations states are available, up to six NRSEG valuesmay be used in AG and NAG computations.

The four NRSEG points shown in FIG. 79 corresponding to fourillumination states are first used to determine whether the featurepairs are acceptable. If the slope of the curve for a feature pair isnegative in some embodiments or generally shows a reversal of direction,the feature pair is unacceptable. If the slope of the line is positiveor monotonic, the feature pair is deemed “acceptable,” and theabsorption gradient for each feature pair is determined by regressingthe NRSEG for the feature pair against the power of light injected intothe tissue for each illumination state of R1, R2, R3 and ALL Rings, andthe slope of the regression line is computed as the absorption gradient(AG) for that feature pair. In an embodiment where the “All Rings”illumination state is not used, the absorption gradient is determined byregressing the log value of the NRSEG for each acceptable feature pairagainst the source-to-detector distance for each ring, which isgenerally proportional to the amount (the power) of light introduced ineach illumination state.

The AGs from all acceptable features (p,q) in an spectroscopic sampleare then normalized and averaged as described above to compute NAG*. Thesuperscript “*” indicates that this NAG value is obtained not from datarelating to subjects used to generate the projection sets and projectorcurves, but from data relating to a person whose glucose concentrationis to be determined. The normalized, averaged, computed slope (or NAG*)may also be denoted by {circumflex over (φ)}. In some embodiments, ahash table mapping may be used find the associated projection curveS_(i), using the Projector Set Mapping

:{{Γ_(H){φ₁}<φ_(1L), φ_(1U)>→S₁{<g_(1L),g_(1U)>, slope₁, y-intercept₁}},{{Γ_(H){φ₂}<φ_(2L), φ_(2U)>→S₂{<g_(2L),g_(2U)>, slope₂, y-intercept₂}},. . . , Γ_(H){φ₉}<φ_(9L), φ_(9U)>}→S₉{<g_(9L),g_(9U)>, slope₉,y-intercept₉}} such that {circumflex over (φ)} is within the limits of[φ_(i) ^(min),φ_(i) ^(max)] associated with S_(i). The computed value ofNAG, {circumflex over (φ)}, is used to select the appropriate curve fromthe set of S₁ to S₉ curves. The determination of S_(i) provides a pairof boundaries (g_(il) and g_(iU)) between which the level of glucose inthe sample lies, and the slope and intercept of the curve S_(i).

Once the S_(i) has been determined, its upper and lower interval valuesmay be used to estimate tissue glucose concentration from spectralmeasurements in conjunction with the average of all normalized Ring 2NRSEG values, y _(C) ²=y_(C) ²*W(i_((p,q))), where y_(C) ² is the Ring 2NRSEG value associated with feature-pair C in the set of all acceptablefeature pairs (p,q), as given by equation (19) and W(i_((p,q))) denotesthe weighting coefficient for that feature pair (as defined above). Inone embodiment, the mapped individual projector curves shown in FIG. 80Bare used to generate glucose values from the Ring 2 NRSEG obtained usingcollision computing. The Ring 2 value of Egain*, described below, wasselected in some embodiments for projection of glucose concentrationbecause Ring 2 most accurately reflects illumination of the dermis,which has the highest concentration of glucose. According to thestructure of the radiation/detection system used, examples of which arediscussed below, different illumination states or sets of illuminationsources may be used in different embodiments.

To compute the glucose concentration level, the following relationshipis used:GL=y _(i)+{(slope_(i)×Ring_2_Egain*))}  (25)where Ring_2_Egain* is the log of the NRSEG from Ring 2, averaged overall the replicates in the illumination sequence, and normalized andaveraged over all acceptable feature pairs in the sample. The process ofusing the slope and intercept of the projection curve to calculate theglucose concentration (analyte concentration, in general) is termed“interpolation,” and this use of that term is distinct from othercontexts herein, where interpolation refers to adding additional pointsto a waveform to extend the length of the waveform in the time domain.In Equation (26)

$\begin{matrix}{{{{Ring\_}2{\_ Egain}^{*}} = {\frac{1}{Nt}\left( {\left. {\sum\limits_{1}^{t}{\overset{\_}{{Ring\_}2{\_\Delta}\;{e\left( t_{p,q} \right)}}*{W\left( {p,q} \right)}}} \middle| {\forall p} \right.,{q\mspace{14mu}{in}\mspace{14mu} N_{t}}} \right)}}\mspace{20mu}{{{Where}\mspace{14mu}\overset{\_}{{Ring\_}2{\_\Delta}\;{e\left( t_{p,q} \right)}}} = {\log\left( {\frac{1}{M}{\sum\limits_{1}^{M}\left\{ {Ring}_{2_{\Delta\;{e{(t_{p,q})}}}} \right\}}} \right)}}} & (26)\end{matrix}$and Ring_2_Δe(t_(p,q)) is the log of net, renormalized spectral gainover all acceptable feature pairs (p,q), M denotes the number ofreplicates, and W(p,q)|∀p,q represents the weighting coefficients thatwere obtained and also used during the AG normalization process, asdescribed above. The glucose value, GL is then output as the estimatedconcentration of glucose.

FIG. 84B depicts flipped individual projector curves S₁ ^(T) and S₂ ^(T)corresponding to the individual projector curves S₁ and S₂, respectivelythat are depicted in FIG. 84A. The point “X” denotes a value Δe,Ring_2_Egain*, obtained from a non-invasive measurement and using anembodiment of collision computing, as described above. A value of NAG,denoted NAG*, is also computed for this non-invasive measurement, asdescribed above. If NAG* falls within [φ_(1L), φ_(1U)] associated withS₁, the flipped individual projector curve S₁ ^(T), i.e., the slope ofS₁ ^(T), and the corresponding y-intercept y1 are used to determine theconcentration of the analyte corresponding to the NRSEG value Δe, i.e.,Ring_2_Egain*. If, however, NAG* falls within [φ_(2L), φ_(2U)]associated with S₂, the flipped individual projector curve S₂ ^(T),i.e., the slope of S₂ ^(T), and the corresponding y-intercept y2 areused to determine the concentration of the analyte corresponding to theNRSEG value Δe, i.e., Ring_2_Egain*.

Thus, for the same value of Ring_2_Egain* different analyteconcentrations can be obtained based on the corresponding different NAGvalues. In various embodiments, the NAG values account for variationsdue to skin properties such as thickness, pigments contained in theskin, etc. The NAG-based determination of analyte concentration thusallows the collision computer to be calibrated universally, i.e.,without needing individualized calibration of the non-invasivemeasurement system for each individual. One of the reasons thetomography-based approach described herein yields accurate analytevalues for virtually all uncharacterized subjects is that the amount ofanalyte represented by the illumination state corresponding to Ring2 canbe distinguished from that represented in other illumination states. Thevariation across different illumination states, represented by the NAG*may be used to select the correct individual projection curve toestimate the concentration of the analyte.

In general, there is a one-to-one mapping between the lower and upperboundaries of Γ_(P) and Γ_(H). It was described above with reference toFIG. 82 that one or more members of Γ_(H) can be Null or do not have anyacceptable feature pairs. A projection set not having any acceptablefeature pairs may also be designated as a Null set. In that situation,the NAG computations used for the mapping process as described above arenot available. Let such a Null member of set of Γ_(H), a membercorresponding to the r^(th) projector set, be denoted by Γ_(H) _(r) .For such members, the range for Γ_(H) _(r−1) may be extended to estimateanalyte concentration over the interval covering the lower boundary ofthe non-Null individual projector curve Γ_(H) _(r−1) to the upperboundary of the one or more contiguous Null members with the highestupper boundary corresponding to Γ_(H) _(r+u−1) , where u=1, 2 . . . , 9or the number of contiguous Null members of Γ_(H).

One likely exception case includes the scenario where there are Nullmembers of Γ_(H) _(r) for the lower/lowest concentrations, such as 20mg/dl-40 mg/dl, 40 mg/dl-50 mg/dl, etc., and for the higher/highestconcentration ranges (e.g., 800 mg/dl-900 mg/dl). In such cases, theestimation range on the lower end and/or on the higher end isextrapolated. The higher end extension is handled in the mannerdescribed above. For the lower end extrapolation, let a Null member ofthe set Γ_(H) be the w^(th) projection set be denoted by Γ_(H) _(w) .For such a member, the range for Γ_(H) _(w+1) is extended to estimateanalyte concentration over the interval covering the lower boundary ofthe non-Null individual projector curve Γ_(H) _(r−1) to the upperboundary of the one or more contiguous Null members, with the highestupper boundary corresponding to Γ_(H) _(r+u−1) , where u=1, 2, or thenumber of contiguous null members of Γ_(H) _(r) .

The overall projection process can thus be summarized referring back toFIG. 73 as follows: (a) The glucose concentrations are varied from 0mg/dl up to 900 mg/dl in 10 mg/dl (or other) increments, and for eachconcentration; (b) The NRSEGs are computed (step 15) via collisioncomputing for all the feature pairs extracted from tissue phantomsamples with different concentrations for the GL and NO-GL featuresdefining the pair. This is performed for all spectra acquired over thecomplete set of illuminations and for all replicates. The NRSEG valuesare partitioned (step 18) into piecewise sub-intervals over the entirerange of concentrations;

Thereafter, (c) using weighting coefficients for each feature pair,computed as described above from pure component spectra of glucose,normalized NRSEG values are obtained; (d) Using all the normalized NRSEGvalues associated with all the feature pairs for all tissue-phantomsamples associated with a particular sub-interval, the slope of theregression line between the normalized NRSEG as the dependent variableand glucose concentration as the independent variable is computed insteps 20, 25, 30, 35, and 40. A single slope is obtained for eachsub-interval;

Then, (e) The slopes are used to plot a concatenated or composite curve“ST” of normalized NRSEG vs glucose concentration at steps 40, 45, and15 through 40; (f) Based on more than 50% changes in the slope of theconcatenated ST curve across the range of glucose concentration, the“points of discontinuity” in the composite (concatenated) curve aredetermined; (g) Using the points of discontinuity the concatenated curveST is partitioned into a number of individual projector curves (e.g.,ST1-ST9);

Thereafter, (h) once the individual projector curves have beendetermined, they are parameterized at step 60. This entailsdetermination of the lower and upper glucose concentration boundariesfor each individual projector curve, flipping of each individualprojector curve, and determining the slope and Y intercept of eachflipped individual projector curve. The boundaries (in terms of glucoseconcentration) of the flipped individual projector curves are used inthe glucose estimation process; The axes of the curve ST are flipped toobtain the concatenated flipped projector curves (“S”) S1-S9, as shownin FIG. 77.

With reference to FIG. 85 (a) boundaries of sub-intervals of analyteconcentration, (e.g., 10 mg/dl, 20 mg/dl, 25 mg/dl, 40 mg/dl, etc., forglucose), over the expected range of variation in analyte concentrationare set in step 10; (b) Tissue phantom samples are selected for eachsub-interval in step 18, and NRSEG values for feature pairs are obtainedin step 15; (c) All NRSEG values are normalized according to the weightscorresponding to the feature pairs, computed or obtained in step 20, andthe normalization is performed for all feature pairs. Non-monotonicNRSEG values according to monotonically changing concentration valuesmay be excluded.

Thereafter, (d) for each sub-interval, a regression line is generated instep 40, where the normalized NRSEG values are plotted against knownanalyte concentration values. Optionally, for each feature pair, NRSEGvalues that are outliers, as described above, may be excluded. The slopeof the regression line is also computed in step 40; (e) The regressionlines (curves in general) are concatenated in step 50, over allsub-intervals, to obtain a concatenated or a composite projector curve.

Then, (f) the points discontinuity in the concatenated or compositecurve, as described above, are determined at step 60; (g) The compositecurve is partitioned into analyte (e.g., glucose) concentrationintervals, according to each point of discontinuity. This may yield one,if there are no discontinuities, or more (e.g., 3, 5, 9, 12, 15, 20,etc.) individual projector curves; (h) The individual curves may beflipped and can be parameterized in terms of analyte concentrationboundaries, slopes, and Y intercepts.

FIG. 86 summarizes the use of a human calibration dataset to completethe mapped projector curve set design. In this process: (a) Theboundaries set for individual projector curves using tissue phantom dataand the process described above with reference to FIG. 85 are used toestablish the piecewise sub-intervals for partitioning the humancalibration data in step 10. These sub-intervals may or may not berelated to the fixed sub-intervals of 10 mg/dl or 20 mg/dl that wereused in the processing of tissue phantom data.

At step 15, the NRSEGs are computed via collision computing for all thefeature pairs extracted from human tissue spectra for both GL and NO-GLfeatures defining the pair. This is performed for all spectra acquiredover the complete set of illuminations and for all replicates. The NRSEGare then partitioned into sets based on the boundaries established instep 10, on the basis of invasively collected reference blood glucosevalues. Some sub-intervals may not have any sample NRSEG valuesassociated with them. As one example, the concentrations of 112, 113,115, and 117 mg/dl may belong to a projector curve bounded by 110-120mg/dl. The interval of a projector curve may be a multiple of 10 mg/dl.

Then, (b) an absorption gradient is computed for each feature pair foreach sample for each interval in step 30 using the process describedabove. Feature pairs with a positive absorption gradient (i.e.,monotonic values of normalized NRSEGs) are considered acceptable featurepairs; (c) The AGs of the acceptable feature pairs are furthernormalized at step 40, using the weighting coefficients obtained at step20 from pure analyte component spectra. The same weighting coefficientsthat are used to compute normalized NRSEG for feature pairs in thetissue phantom calibration data can be used to compute NAG values foreach acceptable tissue spectra feature pair;

Thereafter, (d) the NAG values for acceptable feature pairs for allspectroscopic samples associated with an interval are used to set theminimum and maximum range of NAG to be used in mapping human data with aparticular individual projector curve; (e) The NAG bounds computed instep 60, over all intervals or projector curve boundaries define therelation between human tissue NRSEG and reference glucose concentrationsused in the calibration tissue phantoms. A monotonicity check isperformed at step 70 to ensure that acceptable feature pairs are valid.In summary, the NAG value is used to select the appropriate ProjectorCurve, and the normalized NRSEG value from Ring 2 is used to estimatethe glucose level.

Universal Calibration

Since noninvasive measurement technologies do not employ a chemicalreaction between glucose and a color-producing or electricalcurrent-forming reagent as in conventional invasive blood glucosetesting, these technologies generally require some sort of“calibration,” i.e., establishment of a response factor that converts ameasurement made by the measurement system into a glucose concentrationresult associated with a reference invasive method. Many conventionalnoninvasive techniques use an “individual” (or “personalized”calibration process) in which a response factor is calculated for eachindividual person making measurements with the technique. Thisconventional personalized calibration may require one or more bloodglucose measurements using an invasive blood-based referencemeasurement—the “calibration factor” is typically calculated andretained by the instrument for that patient. Many of these conventionalmethods, owing to physiological variations in the patient over time,usually also require periodic recalibration to prevent errors.

Some known universal calibration techniques generally employ themultivariate techniques described above, but have typically not providedaccurate, consistent, results. In general, these known techniques do notprovide robust universal calibration. For example, a Mean AbsoluteRelative Difference (MARD) of 38%, which is generally considered to beclinically unacceptable, was reported by Lipson, et al. in “Requirementsfor Calibration in Non-Invasive Glucose Monitoring by RamanSpectroscopy,” J. Diabetes Science and Technology, pp. 233-241, 3(2),2009.

These known attempts at universal calibration appear to have relied onthe stabilization of the sensor or measurement device hardware; physicsor physiology-based measurement techniques for normalization; assistedblood perfusion in the tissues; sufficiency of the size of training,validation and cross-validation datasets; and empirical adjustments ofthe training error-minimization threshold, with limited success. One ofthe largest sources of variation among individuals with regard to tissueglucose measurement is skin thickness. As glucose is less than 0.1% ofhuman tissue by weight, variations of skin properties generally producechanges in a spectroscopic signal much greater than the changes due toglucose concentration variations. Variances in a spectroscopic signalmay be further exacerbated by thermal, mechanical, optical and contactvariations. A glucose signal measured in skin typically comes frommultiple tissue layers and from a mix of blood and interstitial fluid,with different skin layers having different concentrations of glucoseand confounders.

Various known methods, due to their inability to reject variations inabsorbance in the background signal from tissue, were often unable tosee different quantities of glucose in two different skin samples asmeasurable changes of absorbance in the NIR spectrum. As a result, theapparent glucose concentration varied depending on the tissue site, withboth variations of the location and over time. In general, it isrecognized that linear approaches, such as multivariate techniques, havenot provided an acceptable universal calibration.

Various embodiments described herein allow for a much more convenientand less error-prone approach by providing factory calibration or“universal calibration:” a measurement and calculation procedure that issufficiently robust to allow analyte (e.g., glucose) measurements to beaccurately made for virtually any person, without the need for anyreference calibration measurements. To successfully compensate forvariations in the composition and thickness of skin layers, the variousembodiments herein can sense and adjust the calculation for each ofthese components in each layer. The collision-computing approach fornon-invasive tissue glucose measurement described herein can achieveuniversal calibration as described below.

Various embodiments for diffuse reflection, tomographic spectroscopicimaging (described below) utilize several photon travel path lengths andacquire NIR absorption spectra in different layers of skin tissue, asshown in FIGS. 87A and 87B, where the imaged layers have varying glucoseconcentrations. Spatial variation in the depths of tissue interrogatedusing different light path lengths (implemented by switching amongdifferent illuminator and detector distances) is shown in FIG. 88, withthe associated mean paths shown in FIG. 89. FIG. 90 shows thedifferences between a subject with thin skin versus a subject with thickskin. Such embodiments of tomographic spectroscopic interrogationillumination system as described herein offers depth controllabilitybelow the skin surface as well as on the skin surface in x and ydirections, thereby allowing a significantly improved subcutaneoustissue volume targeting.

As an example, there is a set of all GL_(Fp) and NO-GL_(Fq), features,where p=1, P and q =1, . . . , Q, represent the total number of GL andNO-GL features as described above, extracted from spectroscopicacquisitions, and associated with subcutaneous tissue volumes of thesimplified three layered skin tissue model of FIG. 87A (as shown in FIG.68 or FIG. 70). Let this set be given by EV_(a)(GL_(p), NO-GL_(Fq)),DV_(b)(GL_(Fp), NO-GL_(Fq)), and, SV_(c)(GL_(Fp), NO-GL_(Fq)), whereepidermal (EV), dermal (DV) and subcutaneous tissue (SV) layers denotesubsurface regions. These tissue regions interrogated during atomographic sequence of illuminations are implemented in someembodiments via a fiber optical probe with a central detection systemand rings of illuminators.

Let the rings Rt: t=1, . . . , T such that T=A+B+C and a=1, . . . , A,b=1, . . . , B, c=1, . . . C, represent the dominant photon travel pathsthrough the epidermal, dermal and subcutaneous tissue layersrespectively. Also, tissue volumes within EV, DV and SV may be furthercomprised of multiple volumes EV_(a1), EV_(a2), . . . , EV_(ax);DV_(b1), DV_(b2), . . . DV_(by); and, SV_(c1), SV_(c2), . . . SV_(cz),respectively (i.e., sub-layers), where each tissue layer is targeted bymore than one illumination source and detection receiver combination ormultiple rings targeting the same layer in the skin tissue. The totalring illuminations are then given by T=X*A+Y*B+Z*C. In such tomographicimaging, our computed differential energy absorption for an individualdermal volume compartment represented as:DVb1(GLp,NO-GLq)|∀EVa1(GLp,NO-GLq),EVa2, . . . ,EVax(GLp,NO-GLq),∀p,q∪DVb2(GLp,NO-GLq)|∀EVa1(GLp,NO-GLq),EVa2, . . . ,EVax(GLp,NO-GLq),∀p,q∪DVby(GLp,NO-GLq)|∀EVa1(GLp,NO-GLq),EVa2, . . .,EVax(GLp,NO-GLq),∀p,q   (27)

This expression represents an example estimator of glucose, asdemonstrated in the glucose estimation results presented below, wherethe MARD value for a group of subjects was numerically less than 15%.The above expression is a representation of the net, renormalizedspectral energy estimated through the collision process for differentfeature pairs in different rings. Given a design of the tomographicprobe, this expression generally represents the total result set fromall features over all illuminations. Computation of the net,renormalized spectral energy gain due to the analyte across differentrings can be described by the above expression.

The probe of FIG. 91, as detailed in FIG. 92, is designed such thattargeting of different skin tissue layers by tomographic sequencesEV_(a1), EV_(a2), . . . , EV_(ax); DV_(b1), DV_(b2), . . . , DV_(by);and, SV_(c1), SV_(c2), . . . , SV_(cz) can be verified based onexamination of acquired spectra based on absorption of spectral bandsknown to be associated with biochemical compounds other than the analyteof interest, (such as by examination of intensity and absorbanceamplitude profiles of the fat, protein and collagen bands as shown inFIG. 93 for different ring illuminations). Profiles of absorptiongradients leading to the assessment of acceptable feature pairs is afunction of the tomographic sequence and the results of the aboveexpression, based on an anatomical and physiological understanding ofskin tissue. The use of multiple illumination-detection pairs to targetthe same layer in the skin tissue, as described above (that is byincreasing the tomographic states), can expand the glucose measurementcapability and increase the ability of the system to compensate for maleand female subjects with varying skin thickness, surface texture, andchanges due to aging, gender, and/or ethnic differences.

Estimation and accumulation of the net analyte (i.e., glucose) spectrum(NAS) signal,

${\Delta\;{\overset{\rightarrow}{e}}_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}},$associated with a specific ring targeting some region of EV, DV or SV,through one or more repeated collisions between appropriatelyconditioned features (extracted from the spectroscopic data acquiredduring a multiple illumination tomographic sequence) and the Zyotonwaveforms, combined with a renormalization step can offset andcompensate for interference due to clutter and scattering losses duringthe propagation of light injected into the skin during each tomographicillumination. Varying tissue volume targeting through the tomographicspectroscopic imaging process described above allows thecollision-computed energy change values, given by the expression

${\Delta\;{\overset{\rightarrow}{e}}_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}},$to represent a robust estimator (an information measure) for the netanalyte signal (NAS) contribution due to glucose, or an analyte, ingeneral. Even though it is extremely difficult to replicate the samplingconditions during estimation to be the same as the sampling conditionsduring collection of calibration data, especially as the skin locationand composition can change each time contact is made, tomographicimaging and collision-computing measurement of the NAS allows foruniversal calibration.

The process of Absorption Gradient (AG) normalization described withreference to FIG. 82 to compute NAG for the purposes of selecting anindividual mapped projector curve, and the associated computation ofNAG, can enhance the accuracy of non-invasive estimations onuncharacterized human subjects by compensating for physiological andtissue differences from the calibration subjects. This is achieved, atleast in part, by weighting the differential absorption from eachacceptable feature pair drawn from different regions of the acquiredspectrum during a tomographic spectroscopic sequence of measurementsthat compensate for variations in subject- and site-specificphysiological and biochemical composition.

While it is an important step for delivering universal calibration in anembodiment using collision computing with multiple features, thecomputation of NAG* is not required for embodiments using only a singlefeature. Normalization of the absorption gradient provides a more robustmechanism for aggregating NAS estimates from different parts of thespectrum as different subjects present tissues with different levels ofconfounders, which can degrade the SCR to unacceptable levels.Computation of NAG* can reduce uncertainty if SCR is degraded, andprovide a more robust estimation of glucose.

The Projection process described with reference to FIG. 78, byreferencing an estimate of NAS obtained through the collision computingprocesses on data acquired using tomographic spectroscopy, to theglucose energy absorption measured by synthetic tissue-phantoms preparedusing known concentration of glucose, allows for universal calibration,such that estimates with a MARD accuracy below 15%, even in the case ofmeasurement of uncharacterized subjects who were not part of anytraining or calibration set, can be obtained. The equivalence of thenet, renormalized spectral energy gain due to glucose in skin tissue ofany individual subject, by creating equivalence of the same level ofenergy absorbed due to glucose presence in a tissue phantom, also helpsto filter variations in human subject measurements.

Tomographic spectroscopy using a number of illumination and detectionelements and optional repeat sequences, followed by collision-computingprocesses with renormalization of post-collision results to obtain aglucose NAS signal estimate, then followed by a projection process, canachieve universal calibration in human non-invasive glucose measurementin various embodiments.

In some embodiments, for the detection and/or quantitation of analytesthat are primarily present in what may be called “sublayers” of tissue(as shown in FIG. 94), a detector geometry with resolution ofsource-detector distances finer than the detector geometry shown for aglucose embodiment in FIG. 69, can be used to differentially interrogatethose sublayers. Some examples include: detection of the presence ofcross-linked collagen or other proteins that accumulate in tissue as theresult of glycation of the proteins from hyperglycemia in diabetes, orin estimation of increase in lactate concentration that is a marker fordetecting onset or progression of sepsis, or in monitoring theoccurrence or progression of melanomas or other skin lesions. Materialsrelated to these conditions are generally known to be present in varyingamounts in different sublayers of the epidermis known as the stratumcorneum, stratum lucidum, stratum spinosum, stratum granulosum, andstratum basale, as shown in the section in FIG. 94. Their concentrationcan be determined using the collision computing methods described here.

In various embodiments, optically targeting specific tissue regionsusing tomographic analysis is accomplished by optimizing theillumination and detection dimensions for the sublayer tissue volume ofinterest. For example, to target various layers of the stratum corneumand epidermis, the illumination-to-detection distance are optimallysmaller than approximately 0.5 mm and the separation of adjacentillumination-to-detection distances are optimally less than 100 μm. Inaddition, due to skin layer thickness and composition differencesbetween measurement locations and individuals, it is beneficial to havea number of distinct illumination-to-detection distances that enableadaptation to anatomical variations of skin.

For example, FIG. 95 represents a two-dimensional optical skinillumination and detection interface with a single 10-μm diameterillumination area, 2, and twelve annular collection regions, 4, eachapproximately 10 μm in width. The detection regions are separated fromeach other by a minimum of 5 μm and the angle of collected light islimited to ±45 degrees by the collection optics. The narrow illuminationand collection widths support volume targeting by limiting thedistribution of illumination-to-detection distances to a maximum rangeof ±20 μm, and the close proximity of the detection regions to theillumination area enables collection of relatively shallow penetratinglight.

The use of twelve different annular detection rings, in the tomographicdetector shown in FIG. 95, allows the optical probe to apply to a widerange of skin types and characteristics, and that the region of interestcan be optically sampled in a number of measurements. The embodimentsfor glucose measurements described above generally require monotonicityover a set of three rings for all samples, but other embodiments mayoptionally use different combinations of rings to establishmonotonicity. Fewer or more than 12 rings can be used in differentembodiments.

A Monte Carlo simulation of skin tissue was performed with the opticalprobe shown in FIG. 95. A plot of the absorbance versus tissue depth anddistance from the point of illumination for the first annular ring isprovided in FIG. 96. In FIG. 95, light is launched downward into theskin within a circle 2 at the origin (the center of the illuminationarea) and diffusely reflected light is collected from the sixth circularring from the center, delineated as “region 6” in FIG. 95, and spanningthe distance 90-100 μm from the center. The darker regions of the plotin FIG. 96 represent higher levels of light absorption and indicate thata very specific volume of tissue is predominantly interrogated between35 and 50 μm below the surface of the skin. The light absorption in thedarker target zone 6 in FIG. 96 is 61.4% per unit volume higher than inthe surrounding tissue.

Similarly, FIG. 97 shows the distribution of photonic absorption for thesecond annular ring with depth of the sampled tissue volume 8 beingbetween 20-30 μm, and the light absorption in the darker target zone ofFIG. 97 is 49.3% per unit volume higher than in the surrounding tissue.A final example is provided in FIG. 98 and indicates that the thirdannular ring is predominately sampling a tissue volume 10 between 45 and70 μm below the skin surface. The light absorption in the darker targetzone in FIG. 98 is 37.8% per unit volume higher than in the surroundingtissue.

Thus, a particular ring or a group of rings can target a specificsublayer of the skin, to facilitate quantitation of an analyte expectedto be present in that sublayer. In some embodiments, such quantitationmay require computation of absorption gradient(s) across a number ofsublayers, e.g., sublayers above and/or below the particular sublayer inwhich the analyte is expected to be present. The additional sublayer(s)across which the absorption gradient is computed can be but need not beadjacent to each other and to the particular sublayer in which theanalyte is expected to be present. Thus, absorption gradient may becomputed across two or more sublayers where at least one interveningsublayer that is not used in the computation of the absorption gradientmay be present between a pair of sublayers that are used in suchcomputation. To facilitate such computation, more than oneilluminator/detector rings can be illuminated according to a selectedsequence, generally called an illumination sequence. As used herein,illumination sequence may represent either or both: a sequence accordingto which the illumination rings are illuminated, and a sequenceaccording to which the detector rings are activated for detection.

Other specific tissue regions, for instance, separation of the papillarydermis from the reticular dermis for detection or measurement of otheranalytes, may be optically sampled by further adjusting the widths ofthe annular rings or restricting the illumination launch angle or therange of collection angles. In the example of the epidermis, targeting ashallow tissue volume, the detection angle may be restricted to between22.5 and 67.5 degrees relative to and facing the area of illuminationvia an optical lens.

In summary, tomographic spectroscopy in conjunction with a non-linearcollision computing processes is used to compensate for variations amongindividuals (and in a single individual over time) of the majorvariables in tissue glucose measurement (skin thickness, skin color, andmost variations in subsurface anatomy and physiology). Calibrationtechniques for glucose measurement established with the processdescribed herein, and with analyte concentrations determined usingdifferent embodiments of the projection system described above, ratherthan being specific for an individual, apply universally to almost allpeople with different, age, gender, and ethnicity. Thus, for essentiallyeveryone, accurate glucose (and other analyte) measurements can beobtained without the need for a personalized calibration procedure orthe periodic recalibration that has been needed for many other known orsuggested noninvasive techniques.

Glucose Results Using Universal Calibration

In some examples, a universal calibration was initially established withtissue phantoms having known glucose concentrations, as described above,and three human subjects with measured reference glucose values. Theresults shown with reference to FIGS. 100 through 103 were obtained (asshown in FIGS. 99A-B) using this calibration for 9 subjects (whosemeasurements and data were not included in the calibration process),with no adjustments or variations in the calibration for any of thesubjects. The agreement shown for the 9 subjects indicates that theuniversal calibration developed produced acceptable agreement withreference measurements for all the subjects.

In various embodiments, the concentration of the analyte and,optionally, other results derived from data-analytic processes, may bedisplayed on a display device and/or may be stored in a database forsubsequent communication to a user, and/or further processing. Forexample, the estimated glucose values may be used for personalizedinsulin dosing decision, insulin bolus optimization, insulinsensitivity, insulin resistance, glycemic resistance, glycemic responsedetermination, hypo- and hyperglycemia monitoring, and metabolic healthassessment. These use-cases are relevant to people with Type 1, Type 2,or gestational diabetes; people with prediabetes, and consumersinterested in wellness measurements.

To summarize the entire projection process, calibration projectorcurves, (as detailed above) which are used to translate the estimatedcollision-computing changes derived from the resulting waveform due to aquantity of the analyte, are generated or obtained in step 16 of FIG.13. For example, in the case of a non-invasive glucose measurement,calibration data is generated in two steps. In the first step, a seriesof in-vitro experiments are performed whereby different, knownconcentrations of the analyte of interest are provided in tissuephantoms which are spectrally imaged using the same hardware and processas used for analyzing the analyte in human subjects. The spectra fromthese tissue phantom samples are processed by the collision computingprocess to show that the resulting, computed spectral energies aremonotonic to the concentration of the analyte. When monotonicity isachieved by refinements of the components of the collision computingprocess, a projector curve set is generated representing concentration(as the independent variable) and spectral energy (as the dependentvariable).

In another data set, a series of measurements are made on one or morehuman subjects, where tissue spectra are acquired along with measuredreference glucose values. Noninvasively measured energy change valuesare then computed which correspond to the reference glucosemeasurements. The conditioning and collision processing fornon-invasively acquired spectra is the same as that used for processingspectral data from tissue phantoms. If monotonicity of the computed net,renormalized spectral energy gain values in relation to the referenceconcentration values is not achieved, the processing of the spectraldata is further refined by one or more of modification of Zyotons,carrier kernels, collision-computing parameters, number of collisioniterations, selection of frequency components in the spectral energycomputation, and changes to the collision operator between collisioniterations. One or more of the entities and/or parameters are revised toachieve a monotonic relationship between spectral energy and analyteconcentration. Once monotonicity has been achieved, the human tissuespectral energy levels are projected or recast in terms of energyabsorptions levels observed from the synthetic medium (e.g., tissuephantom), as described above.

Spectra Acquisition

With reference to FIG. 104A, a spectrum acquisition system used for thedetection and/or measurement of an analyte of interest 2 in an in-vivoor an in-vitro medium 4 typically includes an illumination source 6 forilluminating the medium 4 with NIR. The system also includes aphoto-detector 8 for detecting the attenuated reflected photons, FIG.104A, or the transmitted photons, FIG. 104B. An MIS may be employed bythe illumination source 6 to acquire a set of spectra reflected fromvarying depths of the medium 4 to estimate the analyte of interest 2. Inone embodiment, NIR radiation in the wavelength range from about 1,000nm to about 1,700 nm is used to illuminate the medium 4.

The output of the spectral acquisition process is a series of NIRdiffuse reflectance spectra represented as intensity vectors on awavelength axis spanning the spectral bandwidth of the acquisitionsystem. A reference intensity measurement is acquired for eachillumination in the MIS using a diffuse reflectance standard, and thesereference measurements are also represented as intensity spectra on thesame wavelength axis as the reflectance spectra obtained from the medium4. National Institute of Standards and Technology (NIST) certifiedDiffuse Reflectance Standards are used in some embodiments to calibratethe reflectance measurement of the system. These standards arechemically inert, with typical reflectance values ranging from 2% to99%, and are spectrally flat over the NIR spectrum to +/−4%. A specificexample of a standard used is a Spectralon® Diffuse ReflectanceStandard—which is highly Lambertian, with Spectralon® SRM-99 reflectancematerial being a good Lambertian reflector for use over the wavelengthrange from 250-2500 nm.

Some embodiments utilize a Fourier transform near-infrared (FTNIR)spectrometer (an interferometer) as a processor of spectral NIRradiation to illuminate skin. In near-infrared spectroscopy, NIRradiation is passed into a sample. Some of the radiation is absorbed bythe sample and some of it is either reflected (reflectance, FIG. 105B)or passed through (transmittance, FIG. 105A). The resulting spectrumrepresents the ensemble molecular absorption or transmission, creatingan overall molecular fingerprint of the sample if the sample is a purematerial. In an FTNIR implemented using a Michelson interferometer(FIGS. 105A-105B), light from the polychromatic near-infrared source,such as a halogen lamp, is collimated and directed to theinterferometer. Interferometers typically employ a beam splitter whichtakes the incoming infrared beam and divides it into two optical beams.One beam reflects off of a flat mirror which is fixed in place. Theother beam reflects off of a flat mirror which is attached to amechanism which allows it to move a very short distance (typically a fewmillimeters) toward and away from the beam splitter. The two beamsreflect off of their respective mirrors and are recombined when theymeet back at the beam splitter. Because the path that one beam travelsis a fixed length and the other is constantly changing as its mirrormoves, the signal which exits the interferometer is the result of thesetwo beams “interfering” with each other as the mirror moves. Theresulting signal is called an interferogram (2 in FIG. 106) whichrepresents the Fourier transform of a spectrum.

About 50% of the light may be directed towards the fixed mirror andabout 50% may be transmitted towards the moving mirror. Light isreflected from the two mirrors back to the beam splitter and passes intothe sample compartment. There, the light is focused on the sample. Thedifference in optical path length between the two arms to theinterferometer is commonly known as the retardation. An interferogram isobtained by varying the retardation and recording the signal from thedetector for various values of the retardation. The form of theinterferogram when no sample is present depends on factors such as thevariation of source intensity and the splitter efficiency withwavelength. This results in a maximum at zero retardation, when there isconstructive interference at all wavelengths, followed by series ofwiggles, as shown in FIG. 106. When a sample is present, the backgroundinterferogram is modulated by the absorption bands in the sample.

FIG. 106 depicts a typical interferogram 2 that may be acquired using aFourier transform near-infrared spectrometer (such as of FIG. 105B). Thewaveform 4 represents the corresponding intensity spectrum along thewavelength axis after taking the inverse Fourier transform of theinterferogram, and the waveform 6 represents the correspondingabsorbance spectrum along the wavelength axis after dividing theintensity spectrum by the appropriate reference or background spectrum.In some embodiments, in order to extract the desired spectral features(step 4 of FIG. 37), each acquired intensity spectrum on the wavelengthaxis is transformed to a corresponding spectrum on a wavenumber axis.

Wavenumber units can be denoted by (wn_(s) (k), k: 1, 2 . . . N_(s)) andwavelength units by (wn_(r)(k), k: 1, 2 . . . N_(r)). The units can beinterconverted using the relations:

$\begin{matrix}{{{wn}_{r}(k)} = {\frac{10^{7}}{{wave}_{r}(k)}{\forall k}}} & (28) \\{{{wn}_{s}(k)} = {\frac{10^{7}}{{wave}_{s}(k)}{\forall k}}} & (29)\end{matrix}$The absorbance spectra may be displayed on the wavelength axis or thewavenumber axis. Several features are extracted from the each of theacquired absorbance spectra acquired during an MIS.

Feature Standardization, Deconstruction, and Conditioning

The preparation of spectral data acquired during an MIS for downstreamanalysis using collision computing entails two sub-processes, each withseveral steps. The two sub-processes in some embodiments are: (i)Feature Standardization, Extraction and Complementary Pairing; and, (ii)Feature Conditioning. In various embodiments, feature standardization,extraction and complementary pairing involves the following fiveprocessing steps:

Step (i) Spectrum standardization is performed prior to extraction ofspectral features, and applied to the entire spectrum in the intensityspace. The standardization computation depends on the dynamic range ofthe spectral sensor. Analog-to-digital converter (ADC) dynamic range andgain coefficients may be set such that when the maximum availableradiation is directed to the medium, the detected peak intensities overthe spectral bandwidth (wavelength range) are adjusted to be 80% of thefull dynamic range. The illumination source 6 in FIG. 104A includes anumber of emitters arranged in concentric rings (as shown in FIG. 69),and the emitters in one or more rings can be turned ON selectively. Insome embodiments, maximum radiation can be directed to the medium byturning ON all rings simultaneously.

Step (ii) The intensities detected in response to other, less thanmaximum illuminations (e.g., illumination of one or more but not allrings in the illumination source example described above), are thennormalized with respect to the intensity detected when maximum radiationis directed to the medium. Applied gain settings may be adjusted using asoftware interface. The sensor firmware gains are set such that thesignal-to-noise ratio is maximized, as estimated near the mid-point ofthe bandwidth, e.g., at 1,350 nm. In some embodiments, an additionalstandardization step involves checking for the wavelength (or x-axis)consistency. This can be implemented by using a rare-earth oxide orother known material as a reference, using a peak in its absorbancespectrum to align the wavelength axis.

Step (iii) Background correction generally involves subtraction of darkcurrent response, both from the spectra acquired during illumination ofthe medium to be tested and the reference spectrum for each illuminatedsequence in the MIS. The dark current over the sensor bandwidth can bedetermined by measuring the detector output when it is not activelyexperiencing radiation—i.e., when the NIR illumination source is turnedoff.

Step (iv) In the absorbance computation step, the absorbance of thedetected spectrum for each illumination in the MIS is computed using thereference spectrum associated with that illumination. In one embodiment,if any element of the intensity vector (i.e., a point of the intensityspectrum) obtained by illuminating the medium to be analyzed issubstantially zero (e.g., the intensity value is less than 10⁻⁵), thatelement is set to a specified minimum value (e.g. 10⁻⁵). Using thismodified intensity spectrum for the medium, the absorbance spectrum canbe computed, element by element, e.g., as the negative of the log to thebase 10 of the ratio of the intensity value of an element in themodified intensity spectrum for the medium to the intensity value of thecorresponding element in the associated reference intensity spectrum.

In some embodiments, outlier spectra may be rejected using furthercomputations, if certain conditions are satisfied. For example, in somecases, the minimum minus maximum absorbance in a specified region of thespectrum should be less than a specified threshold, e.g., 0.6. In somecases, the average absorbance over a specified range of wavenumbers iscompared with the average absorbance over a different range ofwavenumbers. If the difference between the two averages is greater thana specified threshold, the entire absorbance spectrum is considered anoutlier and may be discarded.

Step (v) Features are then extracted from the various absorbancespectra. To this end, FIG. 107 shows pure component spectra A-E forselected analytes and confounders (e.g., water, collagen, glucose, urea,and fat). A pure component spectrum is an absorbance spectrum for asubstance (e.g., an analyte or confounder) and can be acquired by eitherusing the pure material or dissolving the substance in distilled water,and measuring a solvent-corrected absorbance spectrum for the substance.In the case of a mixture of substances, pure component spectra for eachof the substances are determined and compared, and wavelength regions(termed “features”) containing concentration information for thesubstances can be determined by inspecting the spectra. For example, thefeature bands 20-26 and 42 are selected to represent concentrationinformation for the analyte and confounding substances.

In various embodiments, the features are divided into (a) features thatcover the spectral region(s) in which the analyte of interestsubstantially absorbs incident radiation described as Con_AN features,(called “GL” features in the embodiments for glucose measurements); and(b) those that do not cover the spectral regions in which the analytesubstantially absorbs radiation, though one or more confounders mayabsorb, even strongly, called NegCon_AN (designated as “NO-GL” featuresin the embodiments for glucose measurement). It is to be understood thatboth Con_An/GL and NegCon/NO-GL features generally include energyabsorbed by one or more confounders, as well as energy lost to noisefrom variations in the concentrations of these confounders and fromscattering.

In the embodiment for glucose measurement, the GL and NO-GL features areselectively paired. This pairing is complementary, in that netdifferential loss in spectral energy in a feature from a region in whichthe analyte absorbs energy can be paired with a feature extracted fromthe same spectrum in a region in which the analyte only minimallyabsorbs energy, and these wavelength regions pairs can be used toestimate the net energy specifically absorbed by the analyte, asdescribed above.

A seven-step process is used in some embodiments for the selection offeatures for analyte determination using collision computing. Step 1—Aninitial minimum feature length of 4 (i . . . , len=4) is chosen and asliding window interval of 4 index positions is chosen (i.e., shift=4).The start of first feature (F₀) is set to the first vector index s₀position, i.e., i.e., the lowest wavelength or highest wavenumber, ofthe individual spectrum acquired in the sequence, i.e., F_(i)={s_(j)_(, . . . ,) s_(j+len)} where F_(i) is the i-th feature with startposition of j; and F_(i+1)={s_(k+shift) _(, . . . ,) s_(k+len+shift)}with k as the start position of the previous feature. F₀={s₀, s₁, s₂,s₃}; Also, the boundaries of analyte absorbance (i.e., glucoseabsorbance) from the absorbance spectrum are established for regionscorresponding to the first, second, or any other spectral harmonics ofthe analyte (known as “overtone regions”) known to be covered by thespectrum (e.g., 1050 nm and 1700 nm). Denote Λ₁={ξ₁₁, ξ_(u1)}; Λ₂={ξ₁₂,ξ_(u2)} where Λ₁, Λ₂, . . . denote the regions covered by the firstovertone (the second spectral harmonic), the second overtone, and anyhigher-order overtones of fundamental glucose absorbances that appear inthe NIR spectrum, with lower and upper spectral boundaries given by ξ₁₁and ξ_(u1) and so on.

Step 2—A set of features is generated by sliding the feature startposition by the sliding window interval. The process is repeated tillthe entire spectrum is spanned and selection of the next feature wouldexceed the last vector index of spectrum. Let the total set of featuresbe denoted by {F₀, F₁, . . . , F_(n)}. Step 3—Spectral energy of eachfeature in {F₀, F₁, . . . , F_(n)} is computed for the entire featurevector. Let the set of spectral energies be denoted by {E₀, E₁, . . . ,E_(n)}.

Step 4—The features are partitioned into two sets: “GL” features, whichrepresent spectral regions of relatively high glucose absorbance, and“NO-GL” features, representing spectral regions where glucose absorbsminimally (these two sets correspond to the PosCon_AN and NegCon_AN setsdescribed above, in general), and correspond to features that aregenerally within the boundaries of known glucose overtone regionabsorption wavelengths (e.g., 1500-1700 nm and 1050-1180 nm) and thosethat are generally outside the boundaries of glucose overtone regionabsorption wavelengths. Features with analyte spectral energies in theupper quartile, in the set associated with glucose overtones, are keptand the rest are discarded. Features with analyte spectral energies inthe lower quartile, in the set not associated with glucose overtones,are preserved and the rest are discarded.

Step 5—Following the optional precursor frequency modulation of thefeature, e.g., with 16.5 Hz, the remaining features (in both the GL andNO-GL sets) are conditioned by using them to modulate a carrier kernelto develop the conditioned feature waveforms. The co-dependencycondition is checked to ensure that it is preserved for each conditionedfeature waveform and the Zyoton, i.e., post-collision dispersal velocityis within a selected threshold limit κ. If the co-dependency conditionis violated for any feature, that feature is discarded. Feature pairingsare formed by coupling a feature (drawn from the GL-set with the highestglucose spectral energy of the modulated feature waveform ((based on theanalyte-information representing, e.g., the first 3, 6, 10, etc.,frequency components))) with a feature drawn from the NO-GL set with thelowest glucose spectral energy of the conditioned feature waveforms.Generally, the GL features are paired with all remaining NO-GL featuresin the set.

As described above, the term

${\Delta\;{\overset{\rightarrow}{e}}_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}},$which represents the relative renormalized spectral energy gain of thezyoton waveform (Z_(r)) resulting from collisions (with a collisioniteration count of

) with a feature extracted from the analyte-absorbing region of theacquired spectrum (e.g., GL_(F) _(p) ) vis-à-vis the renormalizedspectral energy gain of the same zyoton waveform, (Z_(r)), resultingfrom collisions with a different feature extracted from a region knownto be minimally absorbing (i.e., NO-GL_(F) _(q) ), for each illuminationstate (i.e., for each illumination state R_(t), where t=1, 2, 3, ALL isas defined above) is computed, and the values of

$\Delta\;{\overset{\rightarrow}{e}}_{({{GL}_{F_{p}},{{NO} - {GL}_{F_{q}}},Z_{r},R_{t}})}$are arranged in an ordered sequence with increasing energies. In someembodiments, Step 5 may be repeated for two tissue spectra taken from asubject calibration set of spectra (when ALL RINGS were illuminated)where glucose values are separated by 60 mg/dl.

In one example, a spectrum with a reference glucose value of 80 mg/dland another with a reference value of 140 mg/dl from the same randomlychosen subject in the calibration set were used. Let the set of netnormalized spectral energy gains of feature pairs generated usingnon-invasively acquired ALL-RING samples with a reference concentrationof 80 mg/dl and 140 mg/dl respectively be denoted by {L_(p1), L_(p2), .. . , L_(pm)} and {U_(p1), U_(p2), . . . , U_(pm)}. Any feature pairswhere U_(pk) is less than L_(pk), both U_(pk) and L_(pk) were discarded.This generally describes a Regeneration Process. If there are fewer than4 surviving feature pairs, Steps 1 through Step 5 may be repeated bydoubling the feature length. This is continued until the feature lengthbecomes 64 cm⁻¹ for a measuring system resolution of 4 cm⁻¹ (longerlengths may be allowed if the system resolution is lower i.e.,numerically greater than 4 cm⁻¹). Lower sensor resolution typicallyyields longer feature lengths. If again there are fewer than 4 survivingfeatures and the maximum length of 64 cm⁻¹ has been reached, the processmay be repeated with a an increase in the feature length of 4 cm⁻¹. Thusfeature length values of 4, 6, 8, . . . up to 64 cm⁻¹ can be used tocheck that the surviving set has more than four features.

Step 6—Features in the surviving set are then introduced to thecollision computer. Post-collision spectral energies from the firste.g., six frequency components are computed. The same check as in Step 5is performed. In some embodiments, all of the features need to meet thecondition after collision that also met it in Step 5 before collision.If all of the surviving features of Step 5 do not meet the conditionafter collision then the Regeneration Process of Step 5 may be repeated.

Step 7—Features that survive in Step 6 are then applied to the entirecalibration set to check for the monotonicity condition over theconcentration range tested in the calibration set. A minimum of 8features were used in some embodiments (with the highest spectral energyratios computed in Step 6) in Step 7. If the monotonicity conditionfails, then the feature set is augmented by two additional features.This process may be repeated until the number of features in themonotonicity check reaches a preset threshold, e.g., 30, 50, 64, 80,etc.

Sets with more than 64 features were not used in some examples, as theyfailed to give sufficient performance in the NIR spectral band ofinterest (i.e., between 1000 nm and 1700 nm). It has been found thathere are a limited number of spectral regions, in this spectral bandwith 2 cm⁻¹ resolution, where the gradient of the Fisher vector computedusing the Fisher information matrix constructed using examples of purecomponent glucose spectra, was spatially separated from the gradient ofFisher vector computed using Fisher information matrix constructed usingexamples of pure component spectra of known confounders (obtained eitherthrough experiments or digitization of published spectra). This numbercan be higher or lower if a different spectral band and resolution wereconsidered. Also, there is an upper bound on the number of features thatcan be effectively used, as determined using empirical methods ininformation theory such as the use of the gradient of the Fisher vectorof the Fisher information matrix described in this example.

In some embodiments for noninvasive glucose measurement, 22 featurepairs, each with a length of 60 cm⁻¹ was used. The pairing of featurescan be performed based on measured spectra of the analyte andconfounders in a selected band of wavelengths. This complementarypairing can support robust subsequent analysis using collisioncomputing. In some embodiments, a tomographic spectroscopic illuminationapproach, referred to as spectroscopic tomography, in which differentdepths of tissue are sequentially or simultaneously interrogated can beused to advantage, based on knowledge of the concentrations of differentanalyte and/or confounder molecules at different depths.

As shown in FIG. 87A, skin tissue is a heterogeneous multi-layered mediawith optical absorption and scattering properties that vary with respectto wavelength, composition, physiological condition, and anatomicaldimensions. Consequently, even within a single individual, the opticalproperties may differ over time and by measurement position, and as aresult of the physical and optical interaction between the measurementsystem and the sampled tissue site. When light, i.e., an ensemble ofphotons, is launched into the skin tissue, multiple scattering andabsorption events occur as the applied photons encounter cells, cellsubcomponents, fibrous protein structures, fluids, and vascularelements. Therefore, the scattering and absorption properties of eachlayer result from a wide range of individual components, their geometryand composition.

In some embodiments of the non-invasive measurement system using a fiberoptic probe, photons are launched through one or more illuminationfibers to a portion of the skin and collected by one or more detectionfibers that are separated from the area of illumination by a distance,as shown in FIGS. 68-70. During transit from the area of illumination(or photon ingress) on the skin tissue, to the area of collection (orphoton egress), several different types of events are possible. First, afraction of the incident radiation may be specularly reflected from theskin surface due to the change in refractive index between the tissueand the air, optical fiber or optical coupling material. Second,penetrating optical radiation or photons may be absorbed by either theanalyte or confounders, generally after a series of scattering events,and converted to heat or re-emitted. Third, generally following numerousscattering events, the photons may be diffusely reflected to the area ofcollection where they are subsequently transmitted via the fiber opticto a detector element. Other photons may also exit the skin outside thearea of collection of the collection fiber(s) and be lost.

FIG. 87B shows the differential paths taken by exemplary NIR photons asthey are launched from a light source and captured by a detector elementas they emerge from the tissue. Detector positions A and B show theabsorption due to notionally different distributions of moleculespresent in the skin at different depths.

Due to scattering of the applied light, the tissue volume that isoptically sampled includes a relatively large volume that increases withthe distance between the illumination and detection areas. As anexample, a Monte Carlo simulation of light transport in tissue was usedto examine the distribution of photons in a three layer model of skintissue. FIGS. 108A and 108B provide two plots of a cross section of theestimated volume-based distribution of photon absorbance by depth andradial distance from the point of illumination, given specific areas ofillumination (A) and detection (B1 and B2). The shaded areas of theplots represent the level of light absorbance, with darker regionsindicating higher levels of photon absorbance. The X- and Y-axesrepresent the distance from the point of illumination to detection andthe depth from the skin surface, respectively.

In one embodiment, detection region B1 is about 282-482 μm from the areaof illumination, A, while B2 is about 1022-1222 μm away. Due to theclose proximity between regions A and B1, the tissue volume affectingthe light collected at B1 (or the interrogated tissue volume) isrelatively small and shallow compared to that collected at B2.Consequently, the contribution of the upper epidermis layer to the totaloptical signal collected in region B1 is significantly greater than thatof B2. Conversely, the signal collected by B2 is more heavily dominatedby light traversing the lower dermis layer.

Thus, it was determined that greater separation of the illumination anddetection areas leads to deeper penetration of light, lower numbers ofcollected photons due to scattering, higher levels of absorption, and alarger optically-sampled tissue volume. This is further illustrated inFIG. 88, a plot of a simulation of the first to third quartile range ofthe optical path of detected photons at six specificillumination-to-detection distances. As the distance betweenillumination and detection regions is increased, the depth of photonpenetration into tissue also increases and the interrogatedthree-dimensional tissue volume grows.

Consequently, knowledge of the relationship between the opticallysampled tissue volume and the illumination-to-detection distanceprovides a basis for a spectroscopic tomographic optical probe designcapable of discriminating specific analytes that are resident withinknown layers of the skin. For example, for noninvasive optical glucosemeasurement, given the anatomical and optical properties of the tissuevolume under consideration, the probing optic is optimized when a numberof channels, each representing a different illumination-to-detectiondistance, are spaced to appropriately interrogate the tissue.

However, the optically interrogated tissue volume for a fixedillumination-to-detection arrangement generally differs (i) betweensubjects; (ii) from site-to-site (within one subject); and, (iii)through time due to the dynamic nature of skin tissue and physiology. Toillustrate this point, consider the mean path of detected photons as theaverage of the large ensemble of complex photon trajectories traversingthe given distance. The path represents the central trajectory of lightand the median of the optically sampled tissue volume.

Referring to FIG. 89, a plot of the simulated mean path or trajectoryfrom six different illumination-to-detection areas is shown for awavelength of 1550 nm. In this embodiment, each distance represents aring of illumination fibers surrounding a single detection fiber.Although the mean path between illumination and detection areas isrepresentative of the changing trajectory of photons with respect todistance, the cumulative set of photon trajectories is much larger andmore complex.

FIGS. 109-112 show graphical plots of the simulated weighted mean pathor trajectory from illumination-to-detection at a wavelength of 1550 nmfor four different simulated skin tissue samples differing in thicknessand glucose concentration. In all simulations, a fixed tomographicoptical probe was used with six different illumination-to-detectiondistances, each representing a ring of illumination fibers surrounding asingle detection fiber. The plots in FIGS. 109 and 110 were derived froma skin tissue model with a thin dermis (500 μm) and glucoseconcentrations of 80 mg/dl and 300 mg/dL respectively. A representative1.5 mm dermis thickness was used in the simulations leading to FIGS. 111and 112 and the associated glucose concentration of the plots were 80and 300 mg/dl, respectively. Comparing FIG. 109 versus FIG. 110 and FIG.111 versus FIG. 112, there is an imperceptible difference in the photonpaths with more than a three-fold change in glucose concentration.

However, there is a profound difference between the trajectoriesassociated with thin (FIGS. 109 and 110) versus thick skin (FIGS. 111and 112) that is visibly much greater than the change due to glucoseconcentration. The change in trajectories with respect to skin thicknessis a consequence of the varying composition and scattering between skinlayers and, in particular, between the dermis and the subcutaneouslayer. The dermis is approximately 75% water while the subcutaneouslayer is 80% triglycerides (or fat). At the simulated wavelength of 1550nm, it generally known that the absorption coefficient of water is manytimes that of fat.

Consequently, photons are absorbed at a significantly higher rate in thedermis (at 1550 nm) than in the subcutaneous layer. In the case of a1500 μm dermis (FIGS. 111 and 112), the maximum point of the meantrajectories is approximately 800 μm. Consequently, the majority path oflight in all trajectories in the dermis which is approximately 75%water. In the simulated case in which the dermis is only 500 μm thick(FIGS. 109 and 110), photon trajectories penetrate through the dermisinto the subcutaneous layer to a mean depth of about 1200 μm where, dueto the lower rate of absorption, longer pathlengths occur withoutreducing the probability of photons still reaching the detector. Sinceskin thickness varies between and within individuals, a change in thisone parameter contributes greater pathlength variation than that due tophysiologically possible changes in glucose.

It follows that the maximum average depth of penetrating light into thinskin (due to the lower absorbing subcutaneous tissue) is significantlygreater than that of thick skin, as shown in FIG. 90. Further, theoptimal distance for glucose detection, measured on the basis of percentdermal absorbance, will vary significantly between individuals and beshorter for thin skin and longer for thick skin. An exemplarytomographic probe, capable of supporting glucose measurement on avariety of skin types, is shown in FIGS. 91-92, and 113. FIG. 91illustrates aspects of the bifurcated fiber bundle including the sampleside of the probe (View A), the illumination end (View B) and thedetection end (View C).

FIG. 92 describes the design of the sample interface portion of thefiber bundle while FIG. 91 is a diagram of the constructed probe. Thesample end of the tomographic probe has six distinct rings of 200 μmdiameter core multi-mode ultra-low-OH fibers that are used forillumination and a single central 600 μm diameter core detectionmulti-mode ultra-low-OH fiber that is used for detection. Theillumination fibers have an approximate numerical aperture (NA) of 0.22while the detection fiber has an NA of 0.37. By altering theillumination sequence, the tomographic probe can provide spatial andvolumetric discrimination of the optically interrogated tissue sample.

In various embodiments, this arrangement provides a balance between thenumber of distinct illumination-to-detection distances, the illuminationpacking fraction of optical fibers, the percent dermis that is opticallysampled and the signal strength of the collected light. However,numerous other arrangements support varying topographical measurements.For example, an alternate embodiment with similar beneficialcharacteristics (FIG. 70) has a single central illumination fiber with aplurality of surrounding rings of detection fibers where each fiber,ring of fibers, or spatially separated groups of fibers are used tosupply light to a detection element.

In some embodiments, individual rings of the tomographic probe (FIG. 91)are selectively illuminated by imaging a source filament through a wheelcontaining several selective mask positions on to the illumination endof the probe (FIG. 91). FIG. 114 is a diagram of a fabricated mask wheelwith multiple rectangular regions, each of which contains an opticalmask that passes light associated with one or more rings to theillumination ferrule that is illustrated in FIG. 91. By mechanicallyrotating the mask in front of the illumination ferrule, the fibersassociated with individual rings or combinations of rings areselectively illuminated. Other embodiments utilize adaptive optics,individual sources, or modulated light to either alter the illuminatingring over time or to discriminate the originating ring of detectedlight.

The characteristics of the tomographic optical probe were evaluated viathe previously described simulations and through in-vivo reflectancemeasurements. Reflectance was computed as the ratio of the photonscollected by the detection fiber to the photons launched from theillumination fibers (as determined by the use of a standard material ofknown diffuse reflectance) and was determined by dividing the intensity(or power) of the detected light by the intensity (or power) of theilluminating light. Consequently, the reflectance depends on both theoptical properties of skin tissue within the interrogated volume and thegeometry and optical characteristics of the fiber optic probe.

The ring-by-ring reflectance of the probe while in contact with anin-vivo skin sample was measured using a Thermo Scientific Nicolet 6700FTIR spectrometer. The collected intensity spectrum of each ring offibers was ratioed to a background air spectrum (via a diffusereflectance standard) and adjusted according to power measurements andsimulation to produce the reflectance spectra as plotted versuswavelength in FIG. 93. As indicated in FIG. 93, the vast majority oflight (i.e., greater than 99.9% at 1550 nm, where the reflectance isless than 1×10⁻³) is absorbed prior to detection, particularly by waterin the wavelength region near 1450 nm.

For illustrative purposes, the specific values for reflectance andabsorbance at 1550 nm as well as the associatedillumination-to-detection center-to-center distances for each ring,using a selected human subject measurement, are provided in Table 14below. The reduction in detected light with distance is a function ofthe increasing pathlength, depth of penetration and opticallyilluminated tissue volume.

TABLE 14 Typical Reflectance Measurements of Skin Tissue using theTomographic Optical Probe Ring Rt Center-to-Center Illumination (as inexample Distance Reflectance State embodiment) (microns) (1550 nm) R1382 4.24E−04 R2 1 629 1.55E−04 R3 2 875 5.70E−05 R4 3 1122 2.90E−05 R51368 1.50E−05 R6 1615 7.00E−06 ALL Rings R4 = {1, 2, 3} all ONsimultaneously

Volume-based sampling through the tomographic probe can be illustratedthrough a comparison of Ring 1 to Ring 4 and Ring 5 spectra absorbanceof skin tissue, as provided in FIG. 115A. In addition to the significantincrease in absorbance, the Ring 4 and Ring 5 spectrum includes uniquefeatures throughout the spectrum that are significantly larger thanthose of the Ring 1 spectrum. Specific absorbance bands appear larger inthe Ring 4 spectrum at 1210, 1710, 1725 and 1760 nm and the shape of the1650-1850 nm spectral region appears to change due to a significantincrease in optical sampling of the subcutaneous layer.

To accentuate the differences, the second derivative of each spectrumwas calculated and is shown in FIG. 115B. The Ring 1 second derivativespectrum more closely represents the second derivative spectrum ofprotein (e.g., collagen and elastin) as represented in FIG. 115C whichindicates that the epidermis is the primary skin layer that is opticallysampled. However, the Ring 4 second derivative spectrum is dominated bythe same absorbance pattern as that of fat which is plotted in FIG.115C. Since fat is present primarily in subcutaneous tissue, the signaldetected when Ring 4 and Ring 5 are illuminated represents a differentvolumetric compartment. Utilization of all six tomographic channelsprovides further discrimination of the tissue volume underconsideration.

Since each optical measurement of the skin generally samples a differenttissue volume (particularly between skin tissue sites on the body andamong different individuals), the information represented in the varioustomographic channels may change. This requires ameasurement-by-measurement change in the optimized combination ofchannels and differential measurements. Determination of the absorbance,a_(ring,λ), of the optical signal acquired at each ring position isperformed via the following equation:

$\begin{matrix}{a_{{ring},\lambda} = {- {\log_{10}\left( {\frac{x_{{ring},\lambda}}{r_{,\lambda}}\frac{12}{N_{ring}} \times p_{ring} \times \Delta} \right)}}} & (30)\end{matrix}$where λ is the wavelength, x_(ring,λ) is the measured sample intensity,r_(,λ) is the intensity of a 99% diffuse reflectance standard collectedon only Ring 1, N_(ring) is the number of fibers is the ring associatedwith the sample spectrum (FIG. 91), and Δ represents the combinedattenuation due to (1) the distance between the reflectance standard andthe probe and (2) the efficiency of the optical coupling between thedetection fibers and detection element. Since Δ does not change, it ismeasured once after device fabrication.

The average relative illumination power between the fibers of Ring 1 andthe ring associated with the sample spectrum is p_(ring). The ratio ispresent due to non-uniform distribution of the lamp filament across thevarious ring bundles on the illumination end (FIG. 91) of the fiberbundle. Compensation with this ratio through time is necessary due to(1) differences in the average power delivered by the fibers in eachring, (2) changes in the lamp illumination ring intensity through time,and (3) differences in the distribution of optical power when a lamp ischanged.

To illustrate this requirement, power measurements collected at thebeginning (T₀) of a clinical study. at 180 days later, and 270 dayslater were compared to determine how the average power delivered by theoptical fibers of Rings 1-4 changed through time. In Table 15 below, T₀represents the starting point while the two subsequent measurementtimes, 180 days and 270 days, are used to show the percent changesthrough time. Each of the four rings experienced a change in deliveredpower although Ring 2 showed the highest (22.3%).

TABLE 15 Percent change through time of the average power delivered byRings 1-4 of the Tomographic Optical Probe System Ring T₀ Δ, 180 days Δ,270 days 1 100% 5.2% −5.3% 2 100% 6.2% 22.3% 3 100% 1.7% 0.8% 4 100%4.6% 4.6%

Based on Table 15 above, it is expected that the average power deliveredeach ring is likely to change and may be distributed differently giventhe spatial placement of each ring's associated bundle within theillumination ferrule (FIG. 91) relative to the optical source andfilament image. Table 16 below provides an example of average relativepower delivered by the optical fibers of each ring through time. Ring 1,for example, delivered 16.4% more power than the average at T₀ whileRing 3 delivered 132% more light (by design). In addition to this unevendistribution of light by ring, the relative power changed through timein a manner that was different for each ring.

TABLE 16 Change through time in the relative illumination power of Rings1-4 of a tomographic optical probe Ring T₀ 180 days 270 days 1 16.4%24.2% 7.2% 2 −17.6% −11.3% −2.0% 3 132.2% 139.4% 127.7% 4 −1.4% 4.6%0.3%

Dynamically Controlled Illumination States

As scattering dominates light propagation in thick turbid media such ashuman skin tissue, it restricts both resolution and penetration depthwithin that tissue. As NIR photons propagate through the diffusiveregime starting at approximately 1 mm below a human skin surface, theirtrajectories change from ballistic to diffusive due to an increasednumber of scattering events, which makes it difficult to identify, muchless track, photon paths. However, steering such NIR photons (i.e.,without using implanted devices such as fluorescent beads) to controltheir below-skin path of travel and to minimize random scattering, iscomplex and challenging. Consequently, dynamic focusing of light throughdynamic control of illumination states or dynamic variation,illuminator-detector distances or other methods such as described below,may be used in some optical spectroscopy embodiments to offset thevariability due to the variations interactions of light with tissue, andin conjunction with collision computing to analyze glucose and otheranalytes in tissue. Dynamic focusing is achieved in some embodimentsusing controlled light delivery.

In some embodiments, such dynamic focusing is achieved in a variety ofways that include: opto-mechanically or electro-optically varyingsource-detector spacing; opto-mechanically or electro-mechanicallyvarying the size of illumination or detection area on the skin; usingphotorefractive materials such as phase-conjugate mirrors for control ofoptical focusing, or the use of an electrically or RF-modulated dynamiclens capable of changing focus, such as those fabricated with liquidcrystals sandwiched between two pieces of glass. Techniques that do notrequire use of implanted waveguides (such as fluorescent beads ornanoparticles) are classified as noninvasive.

Noninvasive techniques for dynamic focusing include tuning the scatteredlight in phase to maximize the spatial or spatio-temporal density at aspecific location below the skin, or time-reversing (byphase-conjugating monochromatic light) the scattered NIR photons back totheir origin, such as time-reversed adapted-perturbation (TRAP) opticalfocusing through exploitation of intrinsic permittivity variations inthe tissue. Use of TRAP focusing is summarized in Ma C et al., “TimeReversed adapted perturbation (TRAP) optical focusing onto dynamicobjects inside scattering media,” Nature Photonics, 2014, 8(12), pages931-936.

Additionally, dynamic control or dynamic focusing helps offset changingSCR due to time-varying changes of confounder concentrations in thetissue responsible for changes in scattering properties (due tophysiology changes, exercise, dehydration, metabolic stress,post-pharmacokinetic response, infection and other reasons) or due torapidly changing analyte concentration (after a meal or after injectionof insulin).

The net impact of employing dynamic control of illumination light or adynamic focusing strategy, using the apparatus listed above or variantsthereof, is the introduction of new and different illumination states ina tomographic sequence processed with collision computing. Dynamiccontrol of light is a generalization of the tomographic illuminationsequence detailed above.

An embodiment of an apparatus for an optical engine embodiment thatimplements dynamically controlled illumination is illustrated in FIG.116 for the detection of glucose and other biochemical and biologicalanalytes, based on quantitative measurements of optical absorption ofthese species as a function of spatial position in three dimensions,i.e., as a function x, y and z where z is in the direction normal to thesurface of the skin or sample. This embodiment is configured to acquirespectral and spatial optical absorbance data on short time scales, ineffect capturing the spectral dynamics of the analyte and otherbiochemical species of interest. Overall, data are acquired in fivedimensions—three spatial directions x, y, and z, and as a function oftime and wavelength.

The shutter with controllable aperture 20, in front of a radiationelement, such as a tungsten halogen lamp and/or a light-emitting diode10, is used to throttle the number of emitted photons by varying theaperture width. The Controller 90 can also control the power to thelight source and thereby modulate the number of emitted photons andtheir wavelength coverage. The photons allowed through the shutter 20are collimated at 30 and focused onto the entrance aperture of thespectrometer 40. The output of the spectrometer is directed to anoptional one-dimensional (1-D) or two-dimensional (2-D) scanner 50 thatcan steer the NIR photon beam onto the depth focusing lens or microlens70. The scanner 50 can be of a deflecting-mirror type drivenelectrostatically or electromagnetically, or an acousto-optic scanner ifone-dimensional scanning is desired.

The electrostatic and electromagnetic mirror scanners can be of a one-or two-dimensional type. A second microlens may be optionally insertedin the beam path to improve either the light efficiency or thethroughput of this optical design and to focus the light into the sampleand collect the light diffusely reflected from the sample. An additionalmicrolens 75 may be used to modulate the reflected photon collectionarea. The reflected photons are directed to the detector and acquisitionunit 85 which then outputs the spectra to the processing unit. Dynamicfocusing and the quantity of launched photons are managed by Controller90, which may optionally vary shutter aperture, depth of focus, scanrate, and/or scanning position. In some embodiments, lens 70 may beimplemented as a microlens array with a different lens for eachdifferent incident angle of light directed to the skin. Optionally,electronically or acoustically tuned photorefractive material may beplace between the depth focusing microlens 70 and the sample to improveoptical coupling, eliminate optical crosstalk, minimize specularreflection, and control the angle of incidence to the skin.

FIG. 117 shows an apparatus 10, 40 to dynamically vary depth of focus inthe sample for spectroscopic tomography, and thereby change the size ofthe illumination and/or detection spot on the skin. In order to providesampling at different depths, the incoming light is brought into thelens 10 that is attached to the translator that moves in z direction(z_(i)) and can focus the incoming light beam 30 into different depthfrom the sample surface. The diffusely reflected light from the sampleis collected by another detection lens attached 40 that can also bepositioned in z direction (z_(o)) normal to the sample surface.

The different z positions of this translated detection lens enablesampling into different depths and provide different paths of lighttraveling from the illumination path 30 to the detection path 20. Theillumination lens and detection lens can be translated independently ortogether, depending on the desired depth sampling or optical pathsampling. Light can be delivered either through free space or viafibers. The translators suited for this application can beelectromagnetic actuators such as voice coils used in optical recordingdrives, compact drives or DVD's. The size of the illumination spot anddetection spot can be independently changed by moving the attachments.

FIG. 118A shows spatial coverage in the x and y directions using theapparatus of FIG. 117. A fixed illumination spot on the tissue and amoving detection spot are shown in the figure. Optionally, by moving thetranslational stages in FIG. 117, the position of the illumination spotcan be varied in both x and y directions; or alternately the position ofboth illumination and detection spot can be varied in either x or y orsimultaneously in both directions.

FIG. 118B shows how depth focusing can be used to image different tissuevolumes below skin in the z direction. This is achieved by varying theposition of the depth lens 70 in the apparatus of FIG. 116. In someembodiments, the center of the illumination spots can be varied in the xand y directions in increments as small as 2 microns and in 5-micronincrements in the z direction.

FIG. 119A shows an actuator 20 set to position a fiber probe thatdirects light to the skin at an angle of 30 degrees from the surfacenormal. The angle of incidence can be controlled in fine increments downto 2 degrees. FIG. 119B shows an embodiment built to inject light ontothe skin surface at pre-set angles to the surface normal. By using twoseparate lens assemblies used for illumination and detection, asignificant reduction of specularly reflected light from rough skinsurfaces is observed, with an additional benefit of flexibility inselecting large numbers of sub-skin volumes (as in FIG. 118A-118B). The2D scanning mirror used for x-y mapping of sample yields continuous,automated fast scanning, where the depth focusing with z translation(using a voice coil) enables both stand-off and contact acquisition.Such time-separated pulsed acquisition of data instead of steady statedata reduces the complexity of mechanical coupling between theillumination and detection fibers required to implement ringed or fixedillumination states.

A benefit of embodiments employing dynamic controllability of light isthat, as resolution is only diffraction limited, theillumination/detection diameter (as in FIG. 118A) depends only on thewavelength of light used, the focal length and size of the lens. Forexample, for X, Y scanning range of 10 mm, a beam diameter <10 micronwas achieved at 2500 nm wavelength and beam diameter of 4 micron wasachieved at 1000 nm, with thousands of sub-volumes that size (as in FIG.118B) that could be scanned. The achieved resolution can exceed what isachievable by fiber-based systems.

As described above, an illumination state is implemented in variousembodiments by turning on and off multiple illumination sources such asconcentric rings around a detector in an example embodiment. Also, thesimultaneous turn-on condition of one or more illuminators (e.g.,individual illuminators in a ring; groups of illuminators in one or morerings; all the illuminators in a ring; or all illuminators in multiplerings), corresponds to an “illumination state,” denoted R_(t) in variousembodiments. Furthermore, an illumination sequence was designated as I¹,I², and I³, where each I^(n), i.e., an illumination state, can beachieved through a combination of simultaneous turn-on of one or morerings, and post-collision NRSEG Δe_(j) ^(i) correspond to the i^(th)illumination state for the j^(th) feature. The collision-computingframework specified above extends to embodiments with dynamic control oflight and/or dynamic focusing.

In such dynamic focusing embodiments, let each illumination state(I^(n)), that results from any variations, over time a finite timeinterval Δt>0, in one or more of the following:

Variation of (i) the source-detector spacing as a function of time,i.e., |Δ_(spacing)(t)|>0 (as in the example shown in FIG. 118A using theapparatus in FIG. 116).

Variation (ii) of the number of emitted NIR photons changes as afunction of time, i.e., |Δ_(emitted photons)(t)|>0 as achieved byvarying the exposed emitter surface or varying input power to the lightsource or other mechanism (as obtained by varying the shutter aperture10 in FIG. 116).

Variation (iii) of the duration of photon launch or collection time ordetection time window as a function of time, i.e.,|Δ_(emitted photons)(t)|>0 (as obtained by varying the duration ofshutter 10 opening time window in FIG. 116). Variation (iv) of thelaunch angle of emitted NIR photons as a function of time where|Δ_(launch angle)(t)|>0 and where launch angle [−π,+π] (as obtained byvarying the adjustable angle of illumination of fiber probe 20 in FIG.119A). Variation (v) of the NIR photon detector/collector orphotodetector gain over time where |Δ_(photodetector gain)(t)|>0, andwhere such gain is varied over one or more detectors (as obtained byvarying the photodetector gain in 85 in FIG. 116). Variation (vi) of theNIR photon detector/collector area over time, whereΔ_(photodetector area)(t)>0, and where such area is simultaneouslyvaried over one or more detectors (as obtained by varying the focusingdepth Zi in 70 in FIG. 116 or varying the focal length Zo in 75 in FIG.116. Varying focusing depth of illumination beam or focusing lens 75results in variable spot sizes as obtained at the tip of the light beamsas in FIG. 117).

Variation (vii) of the focal length of focusing optics used to focus NIRphotons onto the skin where |Δ_(focal length)(t)>0 (as obtained byvarying the focusing depth Zi 70 in FIG. 116 or varying the focal lengthZo—75 in FIG. 116). Variation (viii) of the spectral bandwidth of theNIR photons launched into the skin or detected after reflectance wherethe bandwidth varies from illumination to illumination and does notexclude one or more spectral features impacting the pairing of GL andNO-GL features used in NRSEG determination (as obtained by changing thescan rate and scan parameters for the spectrometer 40 in FIG. 116).

Variation (ix) of the amount of light delivered to the skin surfacewhere |Δ_(light delivered to skin)(t)|>0 (as obtained by varying thevoltage 12 driving the light source 10, or by changing the shutteraperture 20 or by changing the settings of the spectrometer 40; andVariation (x), application of any skin tissue perfusion assist, such asthrough application of an optical coupling or gel, topical rubefacient,mechanical, RF, or electrical stimulation that varies the water contentof the skin tissue or alters blood flow to the skin tissue.

In some embodiments, an optical diffuse reflectance spectrum collectedduring such dynamically varying illumination states is then (i)deconstructed into features, (ii) conditioned using a carrier kernel,then (iii) collided with a corresponding Zyoton waveform to obtain theNRSEG values, which (iv) which are then projected to obtain analyteconcentration using the process described above. The repeats andreplicate sequences, as described above for an embodiment using afiber-optic ring illuminator system (which is an example of a fixedillumination system with several illumination states), also apply tovarious embodiments employing dynamic illumination and/or with focusing(called “dynamically varying illumination system with severalillumination states). Thus, averaging of NRSEG in processing spectrafrom dynamically varying illumination system with several illuminationstates can be performed in a similar manner as for repeats and replicatespectra obtained using a fixed illumination system with severalillumination states. In various embodiments, analytes may be found inhigher concentrations in, for example, in specific depths, layers, orregions of the medium. In some embodiments for noninvasively determiningglucose in tissue, glucose is found in a higher concentration in thedermis layer than it is in either the epidermis layer above or thesubcutaneous layer below.

An optional refinement of the use of dynamically controlled light isthrough an optical interface to the tissue that allows alteration of theillumination or detection angle by angling optical fibers of aring-based annular probe relative to the perpendicular, to accomplish agreater resolution of interrogated tissue volumes than just thevariations in illumination-to-detection distances used in variousoptical systems described above. Modification of the illumination anglerefers to a change in the angle of launched light from the perpendicularand leads to a change in the distribution of photons inserted into theskin. Hence, modification of the illumination angle can be used totarget a specific tissue volume given the tissue state and structure(e.g., thickness, collagen density, scattering, hydration, etc.).

Modification of the detection angle refers to a change in thedistribution of optical collection angles. For example, with a fiberoptic in contact with, and perpendicular to, the skin, having anumerical aperture (NA) of 0.37, the collection volume can be a conewith an acceptance angle of approximately 22.5 degrees about the lineperpendicular to the skin as illustrated in FIG. 120. A change in thedetection angle refers to a modification of the central collection anglefrom the perpendicular.

FIG. 121 illustrates an optical interface that uses one centraldetection fiber (e.g., 500 μm ultra-low-OH silica fiber) and a series ofannular rings made from angled 200 μm illumination fibers, with a singlefiber from each ring shown. This exemplary optical interface lay-out maybe employed for launching light into the skin at an angle that varieswith the illumination-to-detection separation. The minimumillumination-to-detection distance can be, e.g., approximately 120 μmfrom the edge of the detection fiber to the edge of the closestillumination fiber, and, the illumination angle increases fromapproximately 0 degrees to greater than 45 degrees as theillumination-to-detection distance is increased, for example, from 150μm to approximately 2 mm.

As depicted in FIGS. 121-123, the illumination angle (from theperpendicular) can be modified according to the interaction of lightwith the tissue at varying distances from the central detection fiber,to detect the maximum amount of light from a desired tissue volume.Specific designs may also be defined for optimizing the measurement ofspecific target analytes. Additional design parameters utilizemeasurements of the mean or median pathlengths of light in variouslayers, as determined from simulations of light interactions withtissue.

In some embodiments for non-invasive glucose measurement, designconfigurations include variations based on parameters that optimize oneor more of the following characteristics: (1) Percentage of the totalpathlength of light that is within the dermis; (2) The amount ofreflectance; (3) Product of characteristics (1) and (2); (4) The productof reflectance and the median dermal pathlength, minus the product ofreflectance and the median epidermal pathlength, and also minus theproduct of reflectance with the median subcutaneous tissue pathlength,and; (5) The product of the square root of the reflectance and themedian dermal pathlength, minus the product of the square root of thereflectance and the median epidermal pathlength, and also minus theproduct of the square root of the reflectance and the mediansubcutaneous tissue pathlength. The fifth characteristic is related tothe signal-to-noise ratio of the absorption due to glucose in the dermislayer.

FIG. 122 shows an optical interface layout for preferentially detectinglight at an acceptance angle that depends on theillumination-to-detection separation, where the angle of illumination isvaried. This optical interface uses one central illumination fiber(e.g., 300, 350, 500 or 600 μm ultra-low-OH silica fiber) and a seriesof annular rings of 200 μm detection fibers. The minimumillumination-to-detection distance is, for example, approximately 120 μmfrom the edge of the illumination fiber to the edge of the closestdetection fiber. In FIG. 123, the two prior concepts are combined andboth the illumination and detection angles may be modified. Thisinterface can both deliver light to the skin at different angles andcollect light from the skin at different angles.

As described above, modification of the illumination (or detection)angles provides a means to target particular tissue volumes. As anexample, using a Monte Carlo simulation, the change of the opticallyinterrogated tissue volume when the illumination angle is changed fromthe perpendicular to 45 degrees is illustrated in FIGS. 124A-124Bthrough plots of the distribution of light deposition into tissue, usingan illumination-to-detection distance of 1.6 mm. The y-axis representsthe depth of penetration of light into the skin with the zero pointrepresenting the skin surface. The x-axis represents the distance fromthe point of illumination, where the region of detection is centered ata distance of 1.6 mm and has a width of 0.2 mm.

When light is launched perpendicular to the skin, the distribution oflocations where light is deposited into subcutaneous tissue varieswidely. By launching light at a 45 degree angle, the distribution ofdeposited light is tighter, does not penetrate as far into subcutaneoustissue, where glucose concentration is lower than in the dermis, andpreferentially targets the dermal region. FIG. 124A illustrates acomparison the interrogated tissue volume between a perpendicular photonlaunch, compared to a 45-degree photon launch in FIG. 124B.

An additional Monte Carlo simulation analysis was performed to determinethe optimal illumination angle versus the distance between the point ofillumination and the point of detection for three different skin types(thin, normal and thick). The simulation models of tissue involved fiveskin layers with characteristics described in Table 17 below.

TABLE 17 Summary of optical properties used for the illumination-anglesimulation Papil- Rectic- Subcu- Relative Stratum Epi- lary ular taneousScattering Corneum dermal Dermal Dermal Layer Magnitude Thick- Thick-Thick- Thick- Thick- (relative to Skin ness ness ness ness ness normalskin Type (μm) (μm) (μm) (μm) (mm) thickness) Normal 20 100 400 600 1 1Thin 20 100 250 250 1 0.7 Thick 20 100 500 1000 1 1.3

The simulated detection area was studied using a 600 μm-diameter fiberwith a NA of 0.37, and the illumination area was set as 200 μm. For eachsimulation (for each skin type and illumination-to-detection distance),the optimal illumination angle was determined by the product of mediandermal pathlength and the square root of the reflectance minus theproduct of the square root of reflectance and the median epidermalpathlength and also minus the product of the square root of reflectanceand the subcutaneous tissue pathlength.

The results of the illumination angle vs. the illumination-to-detectiondistance variations are shown in FIG. 125. In the plot, the launch angleis expressed in degrees from parallel with the skin such that aperpendicular launch angle is 90 degrees. Using the calculationsdescribed above, the results indicate that the optimal angle varies withrespect to skin type (thick: >200 microns, thin: <100 microns, andnormal: between 100 and 200 microns in thickness) and that measurementlocations involving higher scattering or thicker dermal layers requirelower illumination angles (i.e., less deviation from perpendicular lightlaunch). On the other hand, optimal illumination of thin skin requireshigher illumination angles (i.e., greater deviation from perpendicular).Simulations were performed to show the optimum illumination launch angleversus illumination-to-detection separation for three different skintypes. In this case, the launch angle is expressed in degrees fromparallel with the skin. As a result, the illumination angle shown herenumerically increases as it varies from perpendicular toward parallelrelative to the skin surface.

Depth and tissue volume targeting may also be optimized by control ofthe distribution of detected light according to angle. For example, FIG.126A-126C illustrates the simulated distribution of light absorbance bylayer for three different detection angles given a fixed 1 mmillumination-to-detection distance. An increase in the detection anglefrom 0 degrees to 40 degrees was found to decrease the percent of lightabsorbed in the subcutaneous tissue in preference to the epidermis anddermis. Additionally, the relative reflectance increased by factors of1.7 and 2.3 times when the detection angle was increased from 0 degreesto 20 degrees and from 0 degrees to 40 degrees respectively.Consequently, modification of the angle of detection was found to enableimproved targeting of the dermis and to increase the total amount ofcollected light measured as relative reflectance. For analytes such asglucose that are preferably detected in the dermal compartment, limitinglight collection to specific angles can provide a significantimprovement in glucose signal strength.

However, the optimal angle of collection generally varies with respectto (1) the illumination-to-detection distance, (2) the wavelength underconsideration and (3) the physical and optical properties of the tissueunder interrogation, such as the skin thickness and a tissue opticalparameter called the scattering coefficient. Determination of theoptimal angle across these three variables can be performed using MonteCarlo simulations and may be applied directly to a particular tissuetype with measured optical properties.

As shown in FIG. 127A-127C, the optimal detection angle for a glucoseembodiment was determined, through Monte Carlo simulation of afive-layer tissue model, on the basis of the percent of the totalpathlength that is within the dermis and the reflectance, for twodifferent skin types with different optical properties, six differentillumination-to-detection distances, and over the wavelength range1100-1800 nm. FIGS. 127A-127C provide plots of the percent increase inreflectance vs wavelength for detection angles ranging between 10 and 40degrees from vertical, and at different illumination-to-detectiondistances. FIGS. 127A-127C show the percent increase in reflectancerelative to that at zero degrees as a function of wavelength for anillumination-to-detection distance of 722 μm; FIG. 127B shows thepercent increase in reflectance versus wavelength for anillumination-to-detection distance of 975 μm, and FIG. 127C shows thepercent increase in reflectance versus wavelength for anillumination-to-detection distance of 1228 μm.

These results indicate that the amount of light collected generallyincreases with increasing detection angle but is also a function ofwavelength and the illumination-to-detection distance. Consequently, anincrease in the detection angle (or illumination angle) will result in ahigher intensity signal. However, the increase in detected light doesnot necessarily correspond to an increase in the analytical signal ofinterest (e.g., the absorption of glucose). Instead, a combination ofthe percent pathlength of detected light passing through the dermis, inaddition to the reflectance, provides a parameter that is related to theSNR of the analyte signal.

To illustrate the dependency of the optimal angle on skin type, the setof simulations was repeated with a thick skin tissue model and theresults are summarized below in Table 2.

TABLE 18 Average optimal collection angle at six illumination-to-detection distances for skin with normal (100 μm) and thick epidermis(300 μm) skin Illumination-to-Detection Normal Skin Thick EpidermisDistance (μm) Optimal Angle Optimal Angle 470 8 0 722 10 1.5 975 20 2.51128 35 10 1480 40 18 1732 42 23

In summary, the illumination and/or detection angles can be used tochange the optically interrogated tissue volume. Based upon the totaldetected light and the percent of light traversing the dermal layer, theoptimal angle varies with respect to wavelength,illumination-to-detection distance and tissue type. Tissue measurementsmade on thinner skin are optimized by setting the illumination (ordetection angles) significantly greater (further from perpendicular)than thicker or higher scattering skin. The optimal angle increases withillumination-to-detection distance.

As described herein, a pairing of NIR illumination and detection centerson skin can create numerous path lengths where different photon travelpaths induce differential scattering and absorption. Both the fixedillumination system with multiple illumination states, and thedynamically varying illumination system with multiple illuminationstates provide a flexible skin surface scanning mechanism with abilityto change optical path length. The resulting spectra may then bedeconstructed into features, conditioned, collided with Zyotons, andtheir energy values projected to calculate concentrations of glucoseand/or other analytes.

In some embodiments, pure component analyte spectra, acquired with thesame instrumentation as that used to measure the analyte, are used as areference for selecting features in regions of stronger and weakeranalyte absorbance. As shown in the feature pairing table in FIG. 49,with reference to FIG. 107, two or more features in the region in whichthe analyte (glucose, in this example) more strongly absorbs energy arepaired with features in a more weakly-absorbing region, to compensatefor high levels of spectral energy absorption due to an unknown,uncharacterized number of confounders also absorbing in the sameregion(s) as the analyte. The number of pairings used may depend on thedegree of confounder interference.

FIG. 83 shows the set of features used in a non-invasive glucosemonitoring instrument, and an embodiment yielding a MARD numericallyless than 15% was achieved in a daily-lifestyle clinical study conductedprimarily with insulin-using subjects with Type 1 diabetes. MARD, asdescribed above, is used as a measure of the degree of clinical accuracyof a new measurement technique when compared to reference measurements.As shown in FIG. 68, the embodiment comprises fiber optic illuminationfibers arranged in a ring geometry with a central detection fiber. Theprobe is detailed in FIG. 69. A total of 34 features was used in thisembodiment, some focusing on wavelengths where glucose is known to bemore strongly absorbing and others in regions where glucose is moreweakly absorbing. Wavelength coverage of features for glucose and someconfounders is shown in FIG. 107. The number of features and length ofeach individual feature is directly related to one or more of thefollowing factors, which provide the design rules.

Factor (a) The number of tomographic spectral scans (where each scanentails illumination through a particular ring or combination of rings);depth penetration of NIR photons in each scan; and the mean path modelof propagation for NIR photons as a function of distance between theilluminator and detector (FIGS. 68 and 69). The propagation mean path,in three dimensions, generally specifies the volume of tissueinterrogated by the radiation in each illumination. For a medium with agiven coefficient of scattering, the number of illumination states andnumber of features generally describe the observability model for themeasurement and the underlying confidence of observing the tissuevolume.

Factor (b) The assumed clutter model and anticipated interference fromconfounders influence the number of features and length. As a designrule, more features are required if the anticipated interference ishigh. Also, a longer feature length is required if scattering isanticipated to dominate the total energy attenuation. Factor (c) Theprediction performance requirements for accuracy and precision, withfeature length proportional to high demand for accuracy and precision.Factor (d) A greater relative ratio of absorbance of glucose in a regionwhere it strongly absorbs to the absorbance of a region of lower glucoseabsorbance requires a longer feature length.

Factor (e) Sensor resolution. If sensor resolution were numericallygreater than 2 cm⁻¹, feature lengths less than 6 cm⁻¹ may lead tonumerical instabilities and should be generally avoided. Depending onthe resolution, the feature lengths can be as long as 256 wavenumbers.In one embodiment used for the study that achieved a MARD of less than15%, the feature length was 60 cm⁻¹. Factor (f) The Zyoton waveformproperties that provide separated glucose results from tissue phantomswith differing glucose concentrations. Factor (g) An anticipated largevariation in optical properties of imaged skin over the populationmandates use of a larger number of features compared to a scenarioanticipating smaller variation.

In various embodiments, paired features which amplify and quantifydifferential energy absorption using the collision computing process areused to determine the energy absorbed by the analyte at variouswavelengths. As the signal of interest, i.e., the net energy absorptiondue to the analyte, is very weak (e.g., less than 0.01% of the totalenergy attenuation in a tissue glucose embodiment), simple differencing(subtraction, linear scaling or ratioing operations) of estimated energyabsorbed in paired combinations of Con_AN and NegCon_AN featuresgenerally does not yield robust analyte concentrations. In fact, asimple differencing can yield errors in excess of 100% of true analyteconcentration in non-invasive measurements. To minimize such errors,various embodiments employ a non-linear, non-invertible collisioncomputation process to estimate energy absorption represented by Con_ANand NegCon_AN features. Differential energy absorption due to an analyteis estimated by combining the energy absorption within the spectralregions identified by the Con_AN and its paired NegCon_AN features, andthe result is used to compensate for variations in the medium in whichthe analyte is measured.

In some embodiments, the NegCon_AN features serve as a proxy forbackground estimation. Complementary pairing can be used to compensatefor sampling variation from illumination to illumination of the same ordifferent media. This can mitigate the effects of instrument or sensordrift, ambient changes in temperature and humidity and sensororientation relative to the medium or the degree of sensor contacttherewith. It is important that, in the tissue glucose embodiment, thesame NO-GL features are paired with different Zyotons, therebyindicating that they are re-used in multiple independent computationalcollisions. One advantage of reusing NO-GL features is a reduction ofthe needed detector bandwidth for glucose detection. Glucose absorptionis broadband and seen, to some extent, in most of the wavelength regionbetween 1000 and 1700 nm. Measurements outside that wavelength windowcan increase detector cost and complexity substantially due to the needfor more expensive materials.

The computed spectral absorbances (based on the reflectance values inTable 14) in the acquired spectra generally correspond to 2 to 5absorbance units, meaning that between 0.001% to 1% of the amount oflight input to the tissue is detected. The bio-optical simulationdescribed above has shown the net absorbance due to glucose (as anexample of an analyte of interest) in optical spectra acquired bysampling the skin tissue to be on the order of 10⁻⁸ to 10⁻⁶ absorbanceunits. As this net absorbance is well below the background noise levelin the spectra, selective amplification of the net energy absorptionchanges due to glucose is essential.

Collision computing is used here to amplify the estimated net energyabsorbed by the analyte over a range of absorbance of up to twelveorders of magnitude to achieve a MARD in estimated versus referenceglucose values numerically less than 15%. To achieve this level ofaccuracy over the range of possible concentration values of glucose inblood or tissue from 20 mg/dl to as high as 1,000 mg/dl, can require thepost-collision dynamic range of the measured spectral energy increasefrom collision computing to be six to eight orders of magnitude toaccurately measure the actual glucose concentration.

Zyotons are thus selected to provide the needed signal amplification ofsix to eight orders of magnitude, and as many as a few hundred thousandrepeated collision iterations may be required to yield a SCR increase ofthis magnitude, i.e., the expected required SCR. The Zyoton frequencybandwidth, the number of collisions, and the carrier kernel are stronglyinterrelated to achieve the expected SCR increase required to achievethe target accuracy. The expected interference due to concomitant NIRenergy attenuation from scattering or spectroscopic confounders presentin the medium sampled by the NIR sensor in the same spectral regions asthe analyte of interest in a particular spectral band (e.g., the 1000 nmto 1700 nm spectral band), the sensor SNR, the specified level ofaccuracy, precision in the estimated analyte concentration, and thesensor sensitivity, stability, and resolution are used to guide theselection and configuration of the Zyotons, the collision-computingparameters, and the carrier kernel parameters used to measure tissueglucose using a tomographic spectroscopy platform, as described above.

The measurement of blood glucose concentration without requiring aninvasive procedure can benefit a large population all over the world. Tothis end, human tissue can be viewed as a medium which containsglucose—the analyte of interest. Several confounders such as water, fat,collagen, and urea, are also present in the human tissue. Variousembodiments of the illumination/detection system (e.g., described abovewith reference to FIGS. 68-70) to direct NIR light to human tissue(e.g., a portion of skin on the arm), to receive radiation reflectedfrom or transmitted through the tissue, and associated embodiments of acollision computer directed to the measurement of blood glucose usingthe received radiation, are described below.

Illumination and Detection Systems for Measurement of Glucose

In various embodiments, a spectrometer can make non-invasive opticalmeasurements of glucose in a patient's tissue using near-infrared light.In an embodiment that is suitable for use in a laboratory setting, theillumination/sensor system may include a near-infrared spectrometer, afiber-optic probe, and an attached computer. The near-infraredspectrometer can be a table mounted Fourier transform infrared (FT-IR)such as a laboratory grade research instrument (Thermo Fisher 6700 FT-IRspectrometer), or a miniaturized system of much smaller dimensions. Insome embodiments, all electrical and optical components, including, forexample, the interferometer, a He—Ne laser used for wavelengthcalibration, a tungsten-halogen source, and optical filters and mirrors,are separated from the patient using an insulated mechanical encasementthat also provides thermal and optical isolation. In some embodiments,the optical system of the spectrometer can block the light from thesource except for wavelengths in the 1000 to 1700 nm range prior tocoupling the light to a fiber optic bundle through an encased mechanicalstage. As a result, only a small fraction of the bulb's energy may beapplied to the patient's arm (e.g., less than 5 mW/mm²).

Light can be delivered and collected through a fiber-optic cable, whichmay be up to 6 feet (or longer) in length. The fiber-optic bundle mayinclude illumination fibers that distribute the delivered energy in apredetermined pattern on the skin surface and detection fiber(s) thatcollect the reflected light and deliver it back to the spectrometersystem for analysis. In some instances, the fiber bundle has anapproximately 1 cm² flat tip or probe that comes into close proximity tothe patient's arm, either with or without an intervening inert andbio-compatible fluid (e.g., Fomblin grease, FC-40 or FC-70 fluorocarbonoil manufactured by 3M). The probe can be mounted on a stand above thedorsal aspect of the patient's arm, which may be resting on a flatsurface (FIG. 99A) or on a cushioned foam pad, such as an arm cradlemanufactured using sponge foam with a leather housing (FIG. 99B). Theprobe stand may optionally include a linear actuator which moves thefiber optic probe close to the patient's arm prior to the start of datacollection.

In some instances, data collection events are initiated by commands froma computer that is attached to the spectrometer, to a linear actuator,and to an encased mechanical stage. The computer may receive thenon-invasive near-infrared measurements from the spectrometer and mayrecord the collected data for subsequent glucose measurement usingcollision computing.

An optical imaging source and detector system as depicted in FIG. 68 canbe used to acquire spectral data from a person's skin and may include afiber optic probe as depicted in FIG. 69. The fiber-optic probe iscoupled to the light source and the detection system in thespectrometer. The probe includes a central detection fiber to capturediffuse reflected NIR light that traverses through and is reflected outof the skin. As shown in FIGS. 68 and 69, a portion of the skin depthcan be illuminated by one or more NIR source arrangements (S₁ throughS_(K)) that are disposed at different distances from the centraldetector fiber e.g., in concentric rings around the central detector.The radiation may traverse through different layers in varying depths ofthe skin, and may be absorbed by the molecules of glucose and anyconfounders located in those layers, depicted schematically by thevarious geometric symbols in FIG. 68.

FIG. 70 shows an alternative design, where the probe has a centralilluminator and a number of detector fibers arranged in rings. While theprobe shown in FIG. 69 may be easier to construct, the probe shown/usedin FIG. 70 can offer greater photon collection efficiency and lightthroughput. The collision-computing processes described above areapplicable to both designs.

Referring to FIGS. 68 and 69, the probe includes a central detectionfiber made from a 600 micron diameter multimodal optical fiber, and sixconcentric rings (R1, R2, R3, R4, R5, R6) of tightly nested illuminationoptical fibers made from 200 micron fibers. FIG. 68 shows the notionallight path for the launched photons through the skin when a transversesection is examined, with rings of greater diameter providing photonswhich reach the detector fiber after generally traversing successivelygreater depths. Different rings can be illuminated in differentsequences.

An example of one illumination sequence is S1, S2, S3, S2, S5, S6wherein the rings R1, R2, R3, R2, R5 and R6 are sequentiallyilluminated. In one embodiment, the path lengths, that is, the distancesfrom the center of the detector fiber to the center of source ring infor the probe are: (S1) 200 μm, (S2) 400 μm, (S3) 600 μm, (S4) 800 μm,(S5) 1000 μm, and (S6) 1200 μm. One or more rings may be used toconstruct an MIS. Also, multiple rings may be simultaneouslyilluminated. The duration of each illumination is one second, althoughshorter or longer durations can be used. One embodiment of an MIS fornon-invasive measurement of glucose is S45, S2, S2, S3, S3, S4, S4, ALLwhere rings 4 and 5 are illuminated simultaneously, followed by ring 2,followed by ring 2, followed by ring 3, followed by ring 3, followed byring 4, followed by ring 4, followed by illuminating ALL rings in theprobe simultaneously. Each illumination generally yields a spectrum inthe 1000 nm to 1700 nm range.

It should be understood that the number of rings used here, and thedesignation of rings or ring combinations to particular illuminationstates is illustrative only. Different numbers of rings, e.g., 4, 10,12, 15, etc., and different designations of rings and/or ringcombinations of two or more rings are contemplated. It should also beunderstood that a ring generally represents a particular set of sourcesof light such as fiber-optic bundles, light emitting diodes, or laserdiodes or alternatively, a set of detectors. This set can be circular,elliptical, square-shaped, rectangular, triangular, hexagonal, etc. Theset can also be one or more segments or an arc of the shapes describedabove. The shape of a ring can be selected according to the size andother properties of the medium to be analyzed and the nature ofdistribution of the analyte and/or one or more confounders therein.

In various embodiments, the interferograms obtained according to the MISdescribed above are converted into intensity spectra corresponding tothe signal reflected from a medium, i.e., the skin, as described above.Parameters, such as the bandwidth and the process employed for thispurpose may be optimized to improve the SNR and data quality fornon-invasive analyte detection/measurement. FIGS. 128A-128B depictdifferent intensity spectra collected when the sample is illuminated ina collection sequence. Specifically, FIGS. 128A-128B show two examples:a high noise example and a desirable low noise example with minimaltissue optical transients. The entire set of signals may be collected ineach acquisition. FIG. 129A shows the intensity spectrum generated fromillumination of ring S₁ shown in FIG. 68. Similarly, FIGS. 129B through129F show the intensity spectra generated as different rings areilluminated, including the combination of two rings (3 and 4 in FIG.129E) and all rings illuminated simultaneously in FIG. 129F.

The light rings may be denoted by a position ID associated with them. Insome instances the system collects data in a particular sequence basedon position ID. For example p (45-5-5-4-4-3-3-All Rings) where the IDs5, 4, 3, 45 refer to the ring number or combination of rings in theillumination sequence. The system can then acquire an intensity spectraassociated with each sequence entry: x_(p,rp,rep)(k), k: 1, 2, . . .N_(s) where pε[positions] is the ordinal ranking of illumination, i.e.,rings 4 and 5 are simultaneously illuminated first and ring 5 isilluminated second in the above sequence; rp is the position (or ring)repeat—for example there are two illuminations of ring 5, two of ring 4in the above example p; and rep is the sample replicate—i.e., the entiresequence performed twice or thrice in succession in the same spectralacquisition.

The total spectral acquisition time is typically a function of thenumber of different illuminations and can use hardware that involvesmovable parts for directing light to the skin. The number of repeats ofthe same illumination position is influenced by instrument drift andillumination source stability over time. Unstable or drifting systemsrequire more repeats. The total number of intensity spectra in the datapacket is P. In one embodiment, full sequence repetitions can be twominutes apart, and can be used to determine a rate of change in glucoseconcentration. Immediate repeats can be averaged to improve accuracy.

An intensity spectrum/vector can be converted into an absorbancespectrum using a corresponding reference spectrum, as described above.In one embodiment, if any element of x′_(p,rp,rep) is equal to zero, itis set to 10⁻⁵. Thereafter, an absorbance spectrum/vector is computedas:

$\begin{matrix}{{{x_{p,{rp},{rep}}^{\prime}(k)} = {\max\left( {{x_{p,{rp},{rep}}^{\prime}(k)},10^{5}} \right)}},{\forall k},p,{rp},{rep}} & (31) \\{{a_{p,{rp},{rep}} = {- {\log_{10}\left( \frac{{x_{p,{rp},{rep}}^{\prime}/x_{r}}}{1} \right)}}},{\forall p},{rp},{rep}} & (32)\end{matrix}$Bars in the Equation above represent absolute values of sampledintensities.

FIG. 129A shows an example of how the absorbance spectrum (on thewavelength axis) is generated using the illumination from ring S₁ shownin FIG. 68 and the above described computation, followed by division bythe background spectrum to generate the absorbance spectrum. SimilarlyFIGS. 129B through 129F show how spectra are generated when differentrings are illuminated, including a combination of two rings (3 and 4) inFIG. 129E and all rings illuminated simultaneously in FIG. 129F. Invarious embodiments, collision computing for glucose concentration isconducted using absorbance spectra on the wavenumber axis. A rare earthoxide standard may be used to calibrate the wavelength axis.

Outlier Rejection in Glucose Spectra

For each intensity spectrum in a data packet used for tissue glucosemeasurement, a step can include determining the degree of contact, whichmay include using the following equations:

$\begin{matrix}{{v_{p,{rp},{rep}} = {\frac{1}{L}{\sum\limits_{k}{x_{p,{rp},{rep}}^{\prime}(k)}}}},{\forall{{k\mspace{14mu}{such}\mspace{14mu}{that}\mspace{14mu} 6873\mspace{14mu}{cm}^{- 1}} < {{wn}_{r}(k)} < {6920\mspace{14mu}{cm}^{- 1}}}}} & (33)\end{matrix}$and L is the number of elements in wn_(r) between 6873 and 6920 cm⁻¹(1455 and 1445 nm). If v_(p,rp,rep) associated with any spectrum isgreater than the threshold, T, the sample may be flagged as being acontact outlier. FIGS. 128B-128A show example spectral profiles whenacceptable patient contact is made and when no-contact is made,respectively. The quality of contact is amplified in the waterabsorption band around 1450 nm.

In instances in which all rings are illuminated simultaneously, themethod may include checking for spectral outliers. In some cases, theminimum minus maximum absorbance in the wavenumber region of 8000-8700cm⁻¹ should be less than −0.6. In some cases, this step can include thefollowing steps using the following equations: The average absorbancebetween the wavenumbers 6873 and 6920 cm⁻¹ is calculated as:

$\begin{matrix}{{h_{p,{rp},{rep}} = {\frac{1}{L}{\sum\limits_{k}{a_{p,{rp},{rep}}(k)}}}},{\forall{{k\mspace{14mu}{such}\mspace{14mu}{that}\mspace{14mu} 6873\mspace{14mu}{cm}^{- 1}} < {{wn}_{r}(k)} < {6920\mspace{14mu}{cm}^{- 1}}}}} & (34)\end{matrix}$where L is the number of elements in wn_(r) between 6873 and 6920 cm⁻¹(1455 and 1445 nm). The average absorbance is calculated between thewavenumbers 7600 and 7800 cm⁻¹ as:

$\begin{matrix}{{q_{p,{rp},{rep}} = {\frac{1}{L}{\sum\limits_{k}{a_{p,{rp},{rep}}(k)}}}},{\forall{{k\mspace{14mu}{such}\mspace{14mu}{that}\mspace{14mu} 6006\mspace{14mu}{cm}^{- 1}} < {{wn}_{r}(k)} < {6061\mspace{14mu}{cm}^{- 1}}}}} & (35)\end{matrix}$where L is the number of elements in wn_(r) between 7600 and 7800 cm⁻¹(1316 and 1282 nm). In some embodiments, if aq_(p,rp,rep)−h_(p,rp,rep)>−0.6 the entire sample is flagged as aspectral outlier. In different embodiments, different wavenumber regionsand/or thresholds may be used according to the properties of theradiation generation and detection hardware and/or the properties of themedium to be analyzed.

Glucose Features

FIG. 107 shows, the features in more and less strongly glucose absorbingregions, and the features that may be used in a collision computing, forexample, in conjunction with a radiation/detection subsystem that usesan Indium Gallium Arsenide (InGaAs) detector configured to operate inthe 1000 nm to 1700 nm range. In one embodiment, each individualfeature, conditioned to provide a corresponding conditioned featurewaveform, is collided with its corresponding Zyoton. A spectrum obtainedfrom each illumination state is deconstructed into 34 features, listedin the Table in FIG. 83, and the overall data package from illuminationsequence of rings #4+#5, #2, #2, #3, #3, #4, #4, #ALL rings produces 272features that may be collided with corresponding Zyotons. FIG. 130 showsan expanded wavelength illustration of one group of features.

Pairing of Glucose and Non-Glucose Features and Zyotons

The pairing used in one embodiment for non-invasive glucose measurementis shown in the table in FIG. 49. The table shows how 22 featurescovering regions in which glucose more strongly absorbs NIR radiationare paired with 11 complementary features covering regions in whichglucose more minimally absorbs NIR radiation, and also with differentZyotons for collisions. The example mapping of features and Zyotons canis shown in the table in FIG. 49.

Each glucose feature (PosCon_GL or “GL”) is paired with a complementaryNegCon_GL (“NO-GL”) feature. Each NegCon_GL (“NO-GL”) and PosCon_GL(“GL”) pair is associated with a specific Zyoton—also specific to aparticular illumination state. Some NO-GL features are paired withseveral different GL features and, depending on the Zyoton pairing,collide with different Zyotons. In some embodiments, the table is loadedinto the collision computer as a master control sequence for collisionsfor each sample (e.g., including several spectra) from the noninvasivetomographic acquisition sequences. Although the table in FIG. 49 listonly 33 feature pairings, more or fewer features and correspondingfeature and Zyoton pairing are possible.

Based on the table in FIG. 49, some examples of collisions for rows 1and 10 of the table in FIG. 49 are shown in Table 19:

TABLE 19 NO-GL-1 

 Z_kernel_E1; GL-1 

 Z_kernel_E1 NO-GL-1 

 Z_kernel_D1; GL-1 

 Z_kernel_D1 NO-GL-1 

 Z_kernel_S1; GL-1 

 Z_kernel_S1 NO-GL-1 

 Z_kernel_MM1; GL-1 

 Z_kernel_MM1 NO-GL-4 

 Z_kernel_E2; GL-10 

 Z_kernel_E2 NO-GL-4 

 Z_kernel_D2; GL-10 

 Z_kernel_D2 NO-GL-4 

 Z_kernel_S2; GL-10 

 Z_kernel_S2 NO-GL-4 

 Z_kernel_MM2; GL-10 

 Z_kernel_MM2

Different features generally represent different levels of spectralenergies associated with their corresponding modulated waveforms (theconditioned feature waveforms) which are also a function of absorbancedue to glucose concentration. Using these features from uncharacterizedsamples with vastly differing analyte spectral energies (spanning 2 to 5orders of magnitude in absorbance space), the post-collision energychange on a feature-by-feature basis can be quite different. Also, asshown in Table 11 above, amount of the incident NIR light entering theskin in a spectroscopic tomographic illumination sequence that yieldsthe spectral dataset can be quite different, depending on theilluminated ring or combination of rings illuminated simultaneously.

Thus, a single Zyoton is often insufficient for colliding with all thedifferent conditioned features generated from different features thatmay be extracted from different spectra acquired during a multipleillumination sequence. Different Zyotons (with different frequencycomponents and/or amplitude profiles) are generally required to amplifyspectral energy absorption due to glucose when analyzing the detectedabsorbance data from different rings. In some embodiments, illuminatedrings R2, R3, R4 and ALL Rings, in an illumination sequence, yield fourdifferent absorbance profiles.

To balance the post-collision changes, to compensate for differences inincident light intensity (depending on the illumination sequence state),and to ensure that co-dependency condition on post-collision dispersionvelocities and waveform divergence are met, 16 different Zyotons withdifferent spectral energies were used in one embodiment for glucosemeasurement. Zyoton kernels E, D, S and MM represent 4 families ofZyoton kernels, i.e., waveform families and/or frequency generators usedin Zyoton synthesis, as shown above in Table 19.

Different spectral energies are associated with the diffuse reflectancedetected during different ring illuminations. Given the radial distancebetween a single illumination ring and central detection fiber in someembodiments, the mean path of NIR radiation below the skin is typicallylimited to the epidermis, dermis or subcutaneous regions. When all therings are illuminated, the light spans all the below-skin layers to anapproximate depth of 2 mm. Different skin layers represent differentbiochemical composition with varying levels of glucose, fat, protein,water, and other compound concentrations. Biochemical models provideguidance for the relative concentrations of tissue glucose in theseregions vis-à-vis each other, and their associated absorbance. Empiricalexperiments of calibration data from human subjects in a controlledclinical study with reference samples was used to build differentabsorbance models for different layers.

These absorbance models indicate that different Zyotons are needed foranalyzing feature data from different illuminations. Also, the featuresfrom each illumination state were further grouped into 4 classes in someembodiments. Each of the classes represented different levels of glucoseabsorbance. This resulted in an overall system of 16 Zyotons as shownwith the Zyoton feature mapping shown in the table in FIG. 49 and thepairing relationship shown above.

As described above, Zyoton kernels E, D, S and MM represent fourdifferent families of kernels with different spectral energies, but whenpaired with the appropriate conditioned feature, the co-dependencycondition was met in the case of each feature. Using the examples givenabove, the total number of feature pairings for each sample analysis is4×22+4×22=(176) using the 16 distinct Zyotons. If the tomographicsequence includes several identical replicates, then the total number ofpairings M is given by the following equation: M=#replicates*2*(#distinct GL & NO-GL feature pairings).

If a collision iteration count of

is implemented, then the total number of collisions, at the featurelevel, is given by M*

. Typical values of

can range from the low tens to 100,000 or more, and numerous collisioniterations are performed in various embodiments, as described above. Inone embodiment,

for the non-invasive detection of glucose measurement in human subjectswas set to be 20,000. As another example,

of 100,000 was used for analyzing glucose in a synthetic tissue phantom.

In general, the number of collision iterations may be determinedaccording to one or more of the following four factors: Factor (i) Thedynamic range of the spectral energy change required between the lowestexpected concentration of the analyte and the highest expectedconcentration of the analyte. Higher dynamic range requires morecollision iterations (also called collisions). As described above,spectral energy changes in each collision iteration are accretive. Thusthe total spectral energy change is typically proportional to the numberof collisions.

Factor (ii) The expected signal-to-clutter increase required: A higherSCR increase requires more collisions, as do more confounders withabsorption in the same spectral band (e.g., NIR region for glucose).Different analytes may require a more even distribution of peak energiesin lower and higher amplitude frequency components of the featurewaveform for all concentrations of the analyte of interest. Morecollisions are often required to separate and amplify absorption energychanges from scattering-induced losses.

Factor (iii) The target accuracy and precision in the estimated analyteconcentration: higher precision and accuracy both require morecollisions, as a higher accuracy requirement translates into a finergradation of the target dynamic range; and Factor (iv) The sensorresolution. Lower sensor resolution generally leads to a requirement forhigher collision counts. Collision count is typically very sensitive tosensor resolution. This factor imposes an inverse relationship betweencollision count and sensor resolution. During a collision computerconfiguration, a collision count of 20,000 may be set for a sensor with0.5 nm resolution for glucose detection, assuming a SCR of 0.0001.

Calibration

For glucose concentration measurement using spectra obtained by NIRillumination of skin, using some embodiments of the non-invasive systemsdescribed herein, the net energy loss due to glucose absorption in thetissue was turned into a glucose concentration using mapped projectorcurves developed from the measurement of subjects and tissue phantomswith known glucose concentrations, as described above. As a singlecomposite projector curve for glucose concentration using this techniquewas found to be nonlinear over the dynamic range needed for human tissueranging from 20 mg/dl to 1000 mg/dl, several overlapping individualcurves, as described above, were used to properly cover the range.

In one embodiment, a collision iteration count of 20,000 was used toaccommodate SCR <0.0001; 0.5 nm sensor resolution, a dynamic range ofspectral energy change of 10⁷, and a MARD goal of under 15%. Thetomographic spectroscopy platform and collision computing methoddescribed above was implemented and evaluated in an institutional reviewboard-approved (IRB) prospective, single-sample correlational designclinical study with primarily insulin-dosing subjects with Type 1diabetes, without controls. The purpose of the study was to evaluate theperformance of the non-invasive glucose monitor described above againstinvasive home-use blood glucose monitors.

The system was trained and calibrated using data collected during three(3) single-day visits by different subjects without diabetes. Readingswere recorded at 15 to 20-minute intervals. At each 20-minute interval,a non-invasive tissue spectral dataset (“sample”) was acquired using thesystem described above and a blood glucose reading was taken from thefinger and from an alternate-site (AS) dorsal side of the subject arm atlocations within 2 to 3 inches from the fiber optical probe placementlocation on the arm. An Abbott Freestyle™ blood glucose meter was usedas a reference system for this study. The estimates of noninvasivelymeasured glucose concentrations were subsequently calculated using thiscalibration for all 9 subjects with the same measurement parameters.

To test the predictability of the system outside the training envelope(e.g., the instrument parameters originally used), several changes weremade in the hardware configuration from the calibration setup whenconcentration calculations were made with this calibration set for agroup of subjects called the “prediction set.” For example, theacquisition time for a calibration set for the entire tomographic samplewas around 4.5 minutes compared to 30 seconds for the prediction set.Also, the instrument used a 2.4μ bandwidth InGaAs detector duringcalibration, versus a 1.9μ bandwidth InGaAs detector at the time ofprediction visits. Also, the calibration data was averaged over 16 scans(with a resolution of 4 cm⁻¹) versus one scan at the same resolution forprediction visits.

The prediction set included a total of 526 data samples acquired over8-to-10 hour, 18-single day visits from the 9 different subjects, with25 to 35 samples per day. The visits were on two consecutive days.Immediately after acquiring the spectrum, alternate-site capillary bloodglucose and finger-stick reference blood glucose concentrations weremeasured. The alternate site location sampled was always on the same armas the spectral measurement, and finger stick measurements alternatedfingers. Throughout the study, the reference values were not provided tostudy personnel who calculated the predicted values until the finalcorrelations were performed.

Demographic breakdown of the subjects is shown in the Table 20 below.Subjects in the prediction set were not part of the calibration set.Subject SUB-6 was reported to have type 2 diabetes, but was totallyinsulin-dependent and treated with an insulin pump and a continuousglucose monitoring system. This subject exhibited minimal c-peptidelevels more typical of type 1 diabetes.

TABLE 20 Demographic Breakdown PATIENT ID GENDER AGE DIABETES TYPE SUB-1Male 12 Type 1 SUB-2 Female 17 Type 1 SUB-3 Male 13 Type 1 SUB-4 Male 16Type 1 SUB-5 Male 59 Type 1 SUB-6 Male 27 Type 2* (c-peptide -) SUB-7Male 17 Type 1 SUB-8 Female 17 Type 1 SUB-9 Male 44 Type 1This was a non-significant risk (NSR) daily life-simulation study inwhich no control was placed on meals, subject activity or insulinadministration, or insulin dosing time. Subjects took two meals per daythat included breakfast and lunch. The estimation results from thecollision-computing based measurement are summarized in FIGS. 100-103,131A-131B, 132A-132B.

Clarke Error Grid Analysis can provide a framework to quantify theclinical accuracy of blood glucose measurements obtained usingexperimental measurements as compared to the blood glucose valuesobtained using a reference measurement (such as YSI, a LifeScan OneTouch™ blood glucose meter, or an Abbott Freestyle™ blood glucose meter,etc.). The Clark Error Grid has become accepted as one of the “goldstandards” for estimating the accuracy of new devices for measuringblood or tissue glucose. The Clark Error Grid breaks down a correlationscatterplot for a reference glucose measurement and an evaluated glucosemonitoring system into five regions: Region A are those values within20% of the reference sensor; Region B contains points that are outsideof 20% but would not lead to inappropriate treatment; Region C are thosepoints leading to unnecessary treatment; Region D are those pointsindicating a potentially dangerous failure to detect hypoglycemia orhyperglycemia; and, Region E are those points that would represent asignificant danger by confusing treatment of hypoglycemia forhyperglycemia and vice-versa.

FIG. 100 shows a Clarke Error Grid comparison of a reference system usedto measure blood glucose from the finger, with the same reference systemused to measure blood glucose from an alternate site, i.e., the arm,illustrating that the two reference measurements agree in accuracy witha MARD of 10.6% and an R value of 0.92.

FIG. 101 shows a Clarke Error Grid comparison of a glucose monitoringsystem utilizing collision computing with a reference system used tomeasure blood glucose from the arm (“alternate site”), illustrating thataccuracy with a MARD of 12.4% and an R value of 0.89 were obtained. Truenoninvasive glucose measurements with this level of precision have notbeen reliably reported with any previously employed system.

As the results in FIG. 101 indicate, using collision computing inconjunction with the projection process detailed herein also yielded avalue of “C80 Accuracy,” (a term generally representing the percentageof glucose levels calculated as below 80 mg/dl that are within ±15 mg/dlof the reference value, and referred to in FIG. 101 as “C80”), of over90% (94.4% in the results shown in of FIG. 101) when the non-invasivetissue measurements were compared to invasive blood glucose measurementsfrom an alternate site.

FIG. 102 shows a Clarke Error Grid comparison of a glucose monitoringsystem utilizing collision computing with a reference system used tomeasure blood glucose from the fingertip, illustrating that accuracywith a MARD of 13.6% and an R value of 0.86 was obtained. In this case,the “C80 Accuracy” figure was over 75% (78.7% in the results shown inFIG. 102) when the non-invasive tissue measurements were compared toinvasive blood glucose measurements from the finger.

FIG. 103 shows a similar comparison of results as in FIG. 102, butcomparing the performance of collision computing based glucoseestimation on a Consensus Error Grid (or Parkes Error Grid analysis)adopted by some clinicians. Consensus error grid assumptions are formedon the basis of five risk levels, which are labeled and described asfollows: A: predicted blood glucose (BG) 20% difference from referenceBG or both predicted and reference B below 70 mg/dl; region B:difference from reference BG within 20% but leads to no treatment orbenign treatment; region C: overcorrection of acceptable BG levels;region D: dangerous failure to detect and treat BG errors; and E:erroneous treatment (i.e., treatment contradictory to that actuallyrequired). All, i.e., 100% of the estimated blood glucose results fromcollision computing were in the A or B region as seen in FIG. 103.

FIG. 131A shows a tracking curve of estimated glucose values obtainedusing collision computing compared to alternate site referencemeasurements. A correlation R of 0.96 was achieved for that visit forSubject 8. FIG. 131B shows the tracking curve of estimated glucosevalues obtained using collision computing compared to finger stickreference measurements. FIG. 132A shows the tracking curve of estimatedglucose values obtained using collision computing for Subject 2 comparedto the alternate site reference measurements. A correlation of 0.94 wasachieved for that visit for Subject 2. FIG. 132B shows the trackingcurve of estimated glucose values obtained using collision computingcompared the finger stick reference measurements for Subject 2, with anR of 0.97.

After the glucose concentration has been determined, in variousembodiments it can be provided to a user, and may also be used inanalytics that include non-invasively predicted hypo/hyperglycemicalarms; determination of insulin sensitivity, insulin response, glycemicresponse, HbA1C, exercise response, wellness information, and fastingglucose levels.

Analysis of Other Types of Data

In addition to the use of spectroscopic measurement data for analysis ofbiochemical analytes in tissue, data from many other spectral, imaging,and other data sources can be analyzed with the collision-computingprocess described herein. The collision-computing and projectionprocesses can be extended to other types of data where the informationsought can be the equivalent of an analyte. Detection and/or measurementof an analyte in this context can be the detection or identificationand/or measurement of any material, property, magnitude, event, anomaly,or condition using or from data acquired from a source. Such data isconsidered to be acquired form a “data-collection domain.”

FIG. 67 includes examples that indicate the diversity of the sources ofother data and data types that may be subjected to thecollision-computing process. In order to process these data using acollision-computing process described in various embodiments, theacquired data can first be transformed to the same data formats as thoseused in the noninvasive glucose example discussed above. Thus, after thetransformation, one or more feature vectors can be represented as x_(w)(1:L) of some finite length L>0 and 0>w>W, where W is the number offeatures, L is feature length, and each element of the w^(th) featurevector, at position i, given by x_(i), is associated with a numericalamplitude value. In its most generalized form, a spectrum can berepresented as a one-dimensional (1-D) amplitude vector where thespectral intensities represent the vector amplitudes, and the vectorindices, e.g., i=1 to 384 correspond to the 1050 nm to 1700 nm NIRregion with a 4-wavenumber instrument resolution, to provide a “semanticvector.” Once data from different sensor types and data streams aretransformed to an analogous representation that includes an amplitudevector and an associated semantic vector, the collision computingprocess can be applied.

Features containing amounts of energy corresponding to the informationsought may be extracted from the source data in the same fashion aswavelength region features are extracted for glucose analysis using aspectroscopic tomography system with a number illumination states. Thesefeatures can selectively represent the property sought, the absence ofthe property sought, and/or the presence and/or quantities of anyconfounders, and such features can be paired with one or more Zyotonsdesigned to correspond to the different features.

As FIG. 67 illustrates, there are many data types or forms,data-collection domains, in general, of physical sensor data, imagingand video data, and computer data objects or tokenized data streams,which can be subjected to the collision computing process. A tokenizeddata stream refers to a human or machine processed, ordered collectionof symbols (numerical, text, or alphanumeric character sets) that havebeen used to replace structured or unstructured data including text(articles, reports, messages, spreadsheets), images, video, audio data,and other sensor data, or any combination of these data types. Many ofthese data modalities involve the measurement of physiologicallyimportant substances or conditions, while others can relate to forms ofphysical data generated by a wide variety of sensors and data sources.

An example that shows the breadth of this approach is the use ofoptical, non-invasive photoplethysmography (PPG) data, which can beprocessed to measure heart rate, heart rate variability (HRV), heartrate recovery (HRR), and pulse transit time (PTT) for blood pressure,respiration rate, oxygen saturation, blood pressure and cardiac outputassessments, neurologically induced skin perfusion changes, brainasymmetry, and also for detecting peripheral vascular disease. Theexample below describes an embodiment for the determination of heartrate.

As described above, one technique of applying collision computing toother data forms is to apply transformations that reformulate such dataand the desired outputs to the data forms and process described abovefor non-invasive glucose measurements. This can be achieved by applyingthe process 2 in FIG. 67 that prepares data for analysis using collisioncomputing. This can be achieved, at least in part, by establishingparallels between data structures (such as features), and thecalibration and projection systems employed in the glucose example. Thisway, rather than establishing entirely new collision computing paradigmsfor each type of data, only a conversion of the other data types intothe spectroscopic data used in non-invasive glucose determination may beperformed, together with refinements of the calibration and projectionprocess as required by the different data formats and the requiredresults.

The initial step 5 of source data modality analysis determines thesyntactic transformations and semantic normalization required to re-castand format different datatypes into a “Normalized Data Format” for usein collisions. Specific syntactic transformations can be different fordifferent data forms such as spectral (e.g., radio frequency, “RF”),thermal or other image data, and magnetic dipole moment (e.g.,gradiometer) data, because the syntax and semantics of data involved indifferent modalities in Unit 10 can be different. For example,electromagnetic data 12, acquired from optical, electromagnetic, RF,nuclear, or mechanical sensors can be spectral data 20, temporal data22, (e.g. from LIDAR), spatio-temporal data 24 (e.g. from radar),spatial data 26 (e.g., from a laser scanner), or symbolic data 28 (e.g.,from a Doppler radar).

Similarly, data from chemical sensors 13, imaging sensors 14, magneticsensors 15, thermal sensors 16, mechanical sensors 17, or acousticsensors 18, can be acquired as spectral data 20, temporal data 22,spatio-temporal data 24, spatial data 26, or symbolic data 28. Locationor geo-location data format can be treated as spatial data or asspatio-temporal data if the geolocation data is also associated with acapture or event timestamp. Collectively, the terms spectral, spatial,spatio-temporal, symbolic, and temporal data are referred to assyntactic modalities. Sensor data collection attributes for a specificsyntactic modality, including the sensor dynamic range, sensorspatial/temporal resolution, sensor SNR, data collection time window,number of collection repeats/replicates can be used to perform sourcedata modality analysis in step 5 to determine the computationaltransformations to generate feature data in a normalized data format.The set of applicable computation transformations represented as 30, 40,50, 60 or 70 are related to the syntactic modalities 20, 22, 24, 26 and28.

For example, if the spectral data are acquired from a single elementspectrometer (e.g., a UV-visible spectrometer, an NMR (nuclear magneticresonance sensor), or an atomic spectrometer) and is in the form of a1-D spectral dataset 32, it can be disassembled into features in aprocess analogous to the glucose example described above. If thespectral data are acquired from a several-detector device such as atwo-dimensional (2D) dispersive spectrometer, a 2-D NMR, or a 2-D-massspectrometer such as MALDI, all of which yield a 2-D spectral dataset36, the data can be disassembled into a number of 1D vectorrepresentations. Similarly, a 3-D mass spectrometer dataset 34 can bedisassembled into a number of 1-D vectors for subsequent disassembly.

Some multi-spectral sensors, e.g., ultrasonic RF sensors for structuralanalysis, that yield n-dimensional spectral data 37, can be referred toas producing N-D spectral data, which can then be transformed into acollection of 1-D spectral representations. Optionally, some sensorssuch as a FTIR spectrometer 35, yield interferograms for eachacquisition cycle, which can be first Fourier-transformed to obtain 1-Dspectra 32 which may be processed further as described above.

Another sensor class, e.g., hyperspectral optical or electro-opticalsensors 38, such as those used in target identification andclassification, provide a 1-D spectrum for each pixel. In such cases,the process of transforming the data to a 1-D spectral representation issimilar to that used for glucose, and may entail two steps to obtainfeatures in some embodiments. The first step applies a pixelsegmentation process to identify and group pixels that are assessed tohave imaged the same object, followed by feature generation from the 1-Dspectral data from all pixels associated with a segmented group ofpixels. Pixels associated with different groups of segments may beprocessed in groups. If the target of interest is not known to beassociated with any pixel of a hyperspectral sensor, then all the 1-Dspectral vectors associated with all pixels may need to be transformedto a collection of multiple 1-D spectral vectors, and each vector maythen be disassembled into features as in the case of glucose example,and then processed further using collision computing.

Temporal data 22 may include geolocation tracks (location of an entityover time) as the form of geolocation positions or amplitude vectors,x(t) over t=1, . . . , T. In the case of geolocation data, it may beoptionally first transformed into distances from a fixed referencelocation in the same coordinate system as the geolocation data. If thetemporal data is from a point sensor 42, such as a single elementcurrent, force, or flow-rate sensor that yields observation withintensity x(t) as a function of time, then the intensity vector may betreated in the same manner as 1-D spectral data 32 and features may bedeveloped by selecting groups of intensities x(t_(i)), . . . ,x(t_(i+p)) over different time intervals of length p, starting at adifferent position i.

A number of sensing elements may be combined to form a 2-D array 46,such as a force or capacitive film sensor. Data from such 2-D sensors 42can be processed as multiple 1-D temporal streams. Similarly, 3-Darrayed temporal sensor data 44, such as data from a 3-axis rate gyro or3-D geophone, may be processed as a collection of multiple 1-D temporaldata streams as in 42. This process may be extended to the case of anN-D arrayed temporal sensor 47, such as a 9-axis multicomponent geophoneused in seismic imaging, which is used to sense the directionally ofp-wave and s-wave acoustic energy returns when optionally used inconjunction with a directional multicomponent energy source. Data fromsuch N-D temporal sensor may be transformed into N 1-D temporal streamswhich may then be individually used for the selection of features.

Some RF sensing systems, such as RF receivers, are used to detect,collect and analyze RF energy in fixed energy bands corresponding todifferent frequencies, 45, over time, but the frequencies of suchRF-detection systems can shift or hop over time. In such cases, the datamay be 1-D or 2-D, but with different semantics of the frequencydimension. Data from such sensors can be treated as multiple 1-Dtemporal data streams, each of which may be transformed into features,and processed using the collision computing techniques described herein.

Some 2-D electro-optical imagers yield hyperspectral system data 48 thatchanges over time, where a 2-D group of pixels are associated with a 1-Dspectrum. Such temporal data streams 36 can be treated as 2-D spectra,with each hyperspectral image processed at each instant of time. Thiscan effectively reduce a 3-D temporal data stream, where each pixel is avector, to specific wavelengths whose intensity value is changing overtime.

Spatial data 26 can be 1-D, for example, a fiber optic strain gauge 62where different locations of the fiber yield a strain measurement. Suchdata, in the form of a 1-D strain intensity vector over time, can beprocessed in a similar manner 42. 2-D arrayed spatial data 66 from CCD,thermal, or ultra-wideband (UWB) imagers may be transformed toconcatenated 1-D spatial data from which features can be extracted. 3-Dsensors such as wave gratings 54 used in imaging may be turned into acollection of multiple 1-D data 52 and processed as 1-D spatial data togenerate features. Hyperspectral imaging sensors 68 may be used todevelop features in a manner analogous to the hyperspectral temporalsensors 48.

Sensor data acquired from spatio-temporal modality sensors 50, where oneor more sensor elements are used to collect data over time, may beprocessed in a manner analogous to the ways temporal or spatial data areanalyzed. A distinction for this modality is optionally fixing thespatial or temporal dimension and then using the other (variable)dimension to generate 1-D vectors from which features may be developed.Examples of 1-D arrayed spatio-temporal sensors 52 include a group ofone-axis accelerometers mounted on a system such as a smart phone, or acollection of microphones in a directional antenna. Visible or thermalvideo 56 is an example of 2-D arrayed spatio-temporal data. N-D arrayedsystems 54 and N-D hopping frequency arrayed spatio-temporal sensors areseen in RF detectors used in RF sensors and directional C-band,microwave, X-band receiver arrays used in surveillance applications.Electro-optical hyperspectral visible video cameras 55 can yieldspatio-temporal data streams in multiple dimensions.

The symbolic data modality 28 is a fundamentally different modality from20, 22, 24 and 26. For example, a symbolic data stream may be generated,for example, from a text stream, document, audio-stream, video-stream,messages, chat, email, observations of events, or activities. Such astream may be parsed and turned into a token stream where symbols areused to represent the presence of words, concepts (as in text or audiodata), activities (as in video) or sightings (as in spot reports), usingan underlying lexicon of tokens TK₁, . . . , TK₂. The entire data streammay then be represented as a temporal stream of tokens TKi as a functionof time TKi(t) 72, which may then be treated as the 1-D arrayed temporaldata 42, and may be referred to as the token stream by assigningdifferent numerical values to each token.

In processing symbolic data, the lexicon is maintained as a semanticdata attribute to retain context, but features may be developed from thetransformed 1-D token stream. If the occurrence or frequency of tokensis more important, then the occurrence or presence of tokens may beturned into a frequency histogram. The frequency histogram then becomesthe proxy for the token data stream and may be used to generatefeatures. In some applications, such as word spotting (i.e., analysis ofan audio stream) to detect specific word occurrences, the audio streammay be directly turned into a frequency histogram 76 and analyzed as anon-tokenized stream. Speech recognition and speech understanding areexamples of applications of data modalities 72 and 76. Spot reports 75are human or machine-generated reports produced by completingpre-designed forms. Completion of pre-designed forms is analogous toconfirming the presence of absence of tokens. Completed reports may thenbe transformed into tokenized or non-tokenized streams of data andtransformed into features. Metadata 74 is analogous to spot reports inthat the presence or absence of attributes may be used to develop tokenstreams 72, which can then be processed.

In big-data applications, data sources may be large database tables,survey forms, audio or video captures (individually referred to assingle-source) or a combination of all of these (multi-source). In suchcases, two preprocessing steps may be used to turn these into ahyperspectral dataset which can then be used for selection of featuresusing the steps 38, 48, 55, or 68, depending on how the dataset isproduced. The two preprocessing steps may include tokenization ofsingle-source or multiple-source data using a single-source lexicon ormulti-source lexicon; followed by conversion to a numericaltransformation 72 of tokens. Geotag streams 78 (such as GPS sightings ofmultiple receivers within a preset geofence or area) may be treated asanalogous to token streams, wherein each received data point is treatedas a token and each sighting treated as an occurrence of a token.

Once the data has been transformed into feature data for the encounteredmodality of a datatype of interest, i.e., format normalization 80, iscompleted, feature data may be generated. This is analogous to featuresextracted from time-domain spectra acquired as in the case of thenoninvasive glucose example. Data 90 may then be output for furtherprocessing by collision computing. Once the entire collision-computingprocess is completed, the semantics of transformation into features maybe used to project the results back to the data-collection domain. Anexample is provided below for the analysis of PPG data (an example of anoptical 2-D temporal data modality 46), using the process and methodsdescribed above.

As an example, the transformation of PPG data to the spectral datarepresentation used for non-invasive glucose can be performed in someembodiments as follows. In the art, PPG is a non-invasive, low-power,biophotonic modality for detection of perfusion or localized bloodvolumetric changes in subcutaneous vessels through skin surfacemeasurements. Blood volumetric changes are inferred by analyzing thetime-resolved Visible-NIR absorption differential between blood and thesurrounding tissue bed that manifest as pulsations with each heartbeat.Exploitation of this phenomenon in PPG modality has found strong utilityin clinical physiological monitoring, vascular assessment and autonomicfunction; specifically the use of a reflectance PPG signal in heart ratemonitoring, With the increase in attention to wearable health andfitness monitoring systems, many investigators have tried to extractreliable information from the PPG waveform, but have been stymied bypoor signal-to-noise ratio, noise and motion artifacts, and the lack ofgenerally available sites on the body that generate reliable PPGsignals.

In some embodiments, to make PPG measurements, the tissue is illuminatedwith visible and/or NIR light from a light-emitting diode (LED) sourceand the resultant scattered or transmitted light is measured with aphotodiode. As described in Allen J (Physiological Measurement, March2007; 28(3); R1-39) and review by Tamura et al, “WearablePhotoplethysmographic Sensors—Past and present”, Electronics 2104, 3,282-302, in FIG. 133, the PPG waveform comprises of a pulsatile (“AC”)physiological waveform attributed to cardiac-synchronous changes in theblood volume with each heartbeat, and is superimposed on a slowlyvarying (“DC”) baseline with various lower frequency componentsattributed to respiration, sympathetic nervous system activity andthermoregulation.

As the tissue is highly perfused, it is relatively easy to detect thepulsatile component of the cardiac cycle. The DC component of the signalis attributable to the bulk absorption of the skin tissue, while the ACcomponent is directly attributable to variation in blood volume in thetissue caused by the pressure pulse of the cardiac cycle as each cardiaccycle of the heart pumps blood to the limbs. Even though this pressurepulse is somewhat damped by the time it reaches the skin, it is enoughto distend the arteries and arterioles in the subcutaneous tissue. Thecardiac cycle refers to a complete heartbeat from its generation to thebeginning of the next beat, and so includes the diastole, the systole,and the intervening pause. The frequency of the cardiac cycle isdescribed by the heart rate, which is typically expressed as beats perminute.

Each cardiac cycle appears as a peak in the signal, as seen in FIG. 134.Because blood flow to the skin can be modulated by multiple otherphysiological systems, the PPG can also be used to monitor breathing,hypovolemia, and other circulatory conditions. Additionally, the shapeof the PPG waveform differs from subject to subject, and varies with thelocation and manner in which the sensor is attached.

PPG generally operates on the principle that volumetric blood changes inthe limb or digit result in changes in the optical density through andjust beneath the skin over a vascular region. Apparatus having a lightsource (e.g., high intensity green light emitting diodes (LEDs) or Redor NIR LEDs) illuminates a small area of the tissue to which atransducer is applied. Light traveling through tissue can be absorbed bydifferent substances, including pigments in skin, bone and arterial andvenous blood. Most changes in blood flow occur mainly in the arteriesand arterioles, compared to the veins. For example, arteries containmore blood volume during the systolic phase of the cardiac cycle thanduring the diastolic phase. PPG sensors optically detect changes in theblood flow volume (i.e., changes in the detected light intensity) in themicrovascular bed of tissue via reflection from or transmission throughthe tissue.

Light scattered and transmitted through the capillaries of the region isdetected by the photodiode, which is shielded from all other light. Asthe capillaries fill with blood, the blood density increases, therebyreducing the amount of light reaching the photodiode. The result causesresistance changes in the photodiode that can be measured and recorded.The two common modes of PPG include a transmissive mode where PPGdevices can be worn on finger, toes, or clamps on ear lobe; and, areflective mode where measurements are made on the cheek, forehead, orin the form of wearables such as watch, bracelet, on arm, legs, etc. Inboth modes, the received signal is assumed to be a measure of volumechanges due to localized blood flow. Transmission mode occurs when theLED source is transmitted through the skin and detection occurs on theother side of the skin. This method can only be done through areas ofthe body thin enough for the photodetector to read a measurable signal.

The second mode, reflection, occurs when both the LED and photodetectorare on the same side of the skin. As the LED emits light, thebackscattered optical radiation from the blood pulsations is detectedand measured. Whether the two components are placed across from eachother across the skin or in parallel to each other on the same side ofthe skin, the photodetector measures the variations in blood pulsationsand outputs a current that is formatted as a voltage for furtheranalysis. Typical implementation of transmissive and reflectance mode isshown in FIGS. 135A-135B with error rates ranging from 2 bpm to 5 bpmduring the resting state (when compared with HR derived from ECG), to 10bpm to 30 bpm during low intensity exercise to 20 bpm to 50 bpm duringhigh intensity exercise. Error rates using collision computing can bereduced to under 3 bpm during resting stage and low intensity exerciseand under 10 bpm during high intensity exercise.

A heart cycle includes two states, i.e., systole and diastole, and theabsorbance is different during these states. Specifically, the intensityof the attenuated light is highest during diastole when the diameter ofthe arterial vessels and hence the absorbance due to the blood volume isminimal, thus showing as a peak in the detected waveform. In contrast,the optical path length in the arteries increases during the systoleperiod until the amount of absorbance reaches a maximum, whichcorresponds to the lower part of the curve in FIG. 133. Hence, theinstantaneous heart rate can be extracted from the time interval of twosuccessive peaks/feet which correspond to the local maximum/minimumpoint of the waveform.

In general, if there exists a λ>0 such that where Φ(t_(i))>Φ(t), where|t−t_(i)|<λ, the value at the point t_(i) is the local maximum point,and Φ(t) is a function that represents the time-varying nature of thePPG waveform as shown in FIG. 134. Consequently we can obtain the timeinterval of two successive peaks: Δt_(i)=t_(i+1)−t_(i), the inverse ofwhich is the instantaneous heart rate. The average heart rate for asequence of n heart cycles can therefore be calculated as:

$\begin{matrix}{{HR} = {\sum\limits_{i = 1}^{n}\frac{1}{\Delta\; t_{i}}}} & (36)\end{matrix}$Here the value of λ is important since it can determine the local rangefor the maximum detection. For example, if it is greater than a heartcycle; only one peak is detected yielding a missing peak, therebymiscalculating the heart rate. FIG. 134 shows a typical PPG waveform andthe local maxima Φ(t_(i)) with respect to the interval λ. In a practicalsetting, the local maximum/minimum points could be obtained viazero-crossing calculation methods through calculating the differencesbetween adjacent elements of the original signal.

As shown in FIG. 136A, some embodiments use one or more green LED lightspaired with light sensitive photodiodes to detect the amount of bloodflowing through the wrist at any given moment. When the heart beats, theblood flow in the wrist and green light absorption is greater; betweenbeats it is less. By flashing the LEDs at a rate of 100 Hz or greater,one can calculate the number of beats in each minute. FIG. 136Bschematically shows a PPG monitor.

FIG. 137 shows the general principle of PPG waveform processing used inthe prior art. Steps included collecting digitized waveform samples overa time window, followed by removal of the DC component and SNRestimation. Analog to digital gain scaling is applied to increase SNR asdesired, followed by averaging to remove noise. When 3 to 5 peaks aredetected, the heart rate is computed by taking the reciprocal of peaksover the time window. Often, the peak detection reduces to determiningthe start and end of a peak in the time domain or frequency domain.

In practical monitoring, the obtained plethysmographic signals might beinfluenced by various noises, e.g., motion artifacts, quantizationeffect, and electrical noise. PPG signal is highly susceptible tomotion-induced signal corruption. Irregular movements, such as tennis orboxing, exacerbate the problem. So the key challenges in PPG processingare cancelling the effects of ambient light, accommodating differentskin conditions and colors, and dealing with physical motion artifacts.Additionally, PPG with traditional measurement techniques can only beused on parts of the body that have a high concentration of bloodvessels (for example, it can be difficult to get a good PPG signal fromthe wrist). Many additional factors, such as Skin perfusion, can affectthe performance of PPG based heart rate sensor. Skin perfusion or theflow of blood in capillaries to the surrounding tissue bed, variessignificantly from person to person and can also be impacted by theenvironment. For example, in colder temperatures, the skin perfusion maybe too low for a PPG-based HR sensor to get a reading. Permanent ortemporary changes to the skin, such as presence of tattoos, lesions, orscars, can also impact heart rate sensor performance.

FIGS. 138A and 138B show the distortion to the PPG waveform during astandstill state and with motion. The transition from standstill tomotion state can typically represent a 20× reduction in SNR of the PPGwaveform in the time domain and 10× in the frequency domain (based onperiodogram distortion for the fundamental frequency). As motion becomesirregular, or there are large changes in the perfusion, the PPG waveformSNR can degrade to below 1:1 or 1:10. In such cases, peak determinationbased on local waveform amplitude or zero crossings is no longer viable.

Collision-computing presents a fundamentally different approach to PPGwaveform processing, e.g., for determination of: heart-rate, heart ratevariability (HRV), heart rate recovery (HRR), pulse transit time (PTT),oxygen saturation by measuring respiration rate measuring, bloodpressure, etc., especially where the SNR is low, e.g., ranges from 1:100to >1:1.

General Principles of PPG Data Analysis Using Collision Computing

In keeping with the principle described above of conversion of otherdata types to mimic spectroscopic data used in non-invasive glucoseanalysis, the PPG analysis process begins with an evaluation of thefundamental differences in data package acquired from a PPG dataacquisition system to that used for glucose. While NIR tissue spectrafor glucose determination are collected as discrete snapshotscorresponding to different illuminations over time (a few millisecondsapart), they are analyzed in a time-invariant fashion; that is, spectraldata are “static” and there is generally no consideration of time in thetissue spectral measurement. PPG data contains time-based information,and the temporal variability is of value in determining the “analyte” ofinterest, which is measurement of heart rate regardless of physicalactivity levels, postural position, or environment. In general, the termanalyte represents a substance of interest that is present in a medium.In the glucose example, blood or tissue is the medium and glucose is thesubstance therein that is of interest, i.e., the analyte in theconventional sense. In the context of PPG however, one analyte is heartrate. Due to the significance of temporal variation in a PPG signal,rather than selecting discrete portions of a spectrum, time slices ofthe PPG signal can be used as “features” for collision computing.

In some embodiments, a PPG system includes L LEDs and P photodiodesoperating in transmittance or reflectance mode as in FIGS. 135A and 135Brespectively. In some embodiments, L=P (i.e., each LED is paired with acorresponding photodiode), while in others L>P (i.e., at least onephotodiode captures the response from one or multiple LEDs illuminatedsimultaneously), or L<P (i.e., at least one photodiode capturesreflected optical signal from more than one LEDS). Let Φ(t,p) representthe time-varying nature of the PPG waveform as shown in FIG. 134, anddetected by the p^(th) LED, for p=1,P and t≧0.

Similar to glucose spectral data, as discussed above, PPG data aresubject to environmental effects, physiological variations due toactivity levels, electronic noise sources, and large confounding effectsthat are grouped together into the term “clutter.” The signal-to-clutterratio (“SCR”) is generally higher than in the case of glucose, but thereis a similar intent to increase it to allow measurement withinestablished clinical and general health monitoring needs. Where thefigure of merit for accuracy in glucose was in one case described asconcentration measurements within 15% of the “true” or reference value,one example of a comparable criterion in heart rate measurement is anerror of under three beats per minute (bpm) as measured in eachfive-to-ten heartbeat periods in resting condition (sitting, standing,sleeping) and under 5 bpm during intensive exercise such as jogging,running, swimming or cycling, as compared to a reference system such aschest band (e.g. Polar V800 with chest strap) or compared to the heartrate derived from ECG measurements.

The basic separation of PPG signals into features equivalent to spectralfeatures used in analysis of glucose begins with the identification of aPPG signal waveform feature related to each pulse cycle of the heart.When the beat is regular and the signal is strong, as in FIG. 134, anynumber of signal-processing approaches can be used to determine when acycle begins. Current signal processing techniques for PPG processing,specifically waveform characterization for Min-Max, peak-to-peakinterval, or pulse shape analysis include digital filtering, stochasticfiltering, auto-regression, empirical mode decomposition, Kalmanfilters, wavelet decomposition, matched filters, neural network andfuzzy logic.

These approaches can determine beat events. Also, more recently 1-axisor 3 axis accelerometer data has been used to identify mode (such aswalking, sleeping, running) and then combine with more traditionalsignal processing methods to better estimate HR. A key challenge withall conventional techniques is severe reduction in efficacy as signal tonoise ratio decreases for any reason, which results in over- orunder-counting peaks associated with the heart rate events. Since boththe interval between cycles and the time of appearance, intensity, andduration of intermediate signals are of interest, care must be taken touse adaptive criteria, especially when signals are noisy, as shown inFIGS. 139A-139B.

When a selected traditional signal-processing technique indicates thestart of a cycle, data can be acquired in varying lengths up to andbeyond the inter-cycle timing period expected from observations ofprevious cycles. The time periods range from about two seconds for thelowest heart rate usually encountered to less than 200 milliseconds forheart rates up to 300 beats per minute, but in each case, the intervalcan be “sliced” into shorter subintervals that contain (or encode) theinformation of interest. One such piece of information is the locationand depth of the “dichrotic notch” 4 that occurs between the two primarypeaks of the pulse cycle, as shown in FIG. 134. Other information, suchas heart function and blood pressure measurements, rely on thecomparison of time of appearance, duration, and amplitude of observedshapes occurring during the pulse cycle.

By conditioning the time features extracted from a PPG signal with acarrier kernel (one designed for this embodiment to incorporate thespecific frequency-domain components sought for amplification), eachfeature can be converted to a conditioned feature similar to that donefor glucose. The conditioned feature can then be repetitively collidedwith a single or different Zyotons, also specifically designed for thefrequency components intended to be amplified. A priori knowledge of theinfluences exerted by known conditions (such as due to malfunction ofthe heart including arrhythmia, coronary artery disease (CAD), angina,and cardiomyopathy) to be determined are used to guide the selectionprocess for the features, the carrier kernel, and the Zyoton. After asufficient number of collision iterations (generally less than innoninvasive glucose measurements owing to higher SNR and SCR of thesedata), the NRSEG for each feature is combined by a process similar tothat used for glucose, in order to produce an equivalent net analytesignal (NAS) for the “analyte,” i.e., heart rate, desired to beextracted from the PPG data.

Using a projection system similar to that of glucose, where PPG dataacquired from subjects with known degrees of known conditions are usedto create the projector curves as in glucose measurement, the quantityor degree of the analyte can be determined with the desired degree ofaccuracy. In the example of heart rate determination, the humancalibration set may include subjects measured at rest and in variouslevels of exercise, with the reference heart rate measured by an ECGsignal detector. Similarly, absorption gradients using NRSEG, theconcept of the Normalized Absorption Gradient, and the projection toactual values for subject samples can be performed using projectionstructures equivalent to those employed in the glucose embodiment above.

EXAMPLE OF HEART RATE DATA

The general appearance of a PPG waveform is shown in FIG. 140, with timeon the horizontal axis, and a form of intensity on the Y-axis. Theintensity can correspond to transmitted light, reflected light, or otheroptical signal intensity. FIG. 141 summarizes the process for computinga heart rate from a PPG sensor using the collision computing apparatusdescribed in this invention. The process can be used to analyze the PPGpulse waveform, Φ(t,p) from some sensor, say the p^(th) photodiode in anmeasurement system having one or more photodiodes for recording thereflected or transmitted light from an LED source.

The system can be operated in continuous-pulsed mode (where LEDsilluminate the skin at a preset on-off frequency) or in an episodic modewhere LEDS are switched on-off for some interval, say for 15 seconds(the “episodic window”) every 10 minutes (the “episodic gap” or“episodic displacement interval”); or for 5 seconds every minute; oreven for 60 seconds every hour. The on-off frequency may range from 5 HZto 256 Hz, while an episodic window could range from 3 seconds to 30seconds), and an episodic displacement interval could range from 1minute (during intensive exercise or a cardio workout such as aerobics)to 6 hours. The LED on-off frequency, episodic window, and episodicdisplacement interval can be explicitly configured by a user and/or maybe configured using software, based on a user announcement (such asstart of workout such as running, walking, cycling, swimming), or may beconfigured automatically using sensors such as 3-axis or angularaccelerometers that determine type, intensity and duration of activity.

With reference to FIG. 141, in one embodiment for heart-ratedetermination, the logic for establishing on-off frequency (Ω in Hz),episodic window (EW in seconds), and episodic displacement interval (EDin seconds) for heart rate computations is received in step 5. Heartrate processing initiates when a start trigger input is received at step10, and a PPG waveform is recorded. The digitized PPG waveformamplitudes Φ(t,p) where t=1, . . . , T where T=Ω*EW, and p correspondsto the p-th photodiode source generating the PPG waveform data stream inthe time domain are extracted at step 15. Depending on the subject'sactivity, HR may vary over the EW, but each beat duration is typicallysome multiple of 1/Ω seconds. In one embodiment, T is set to 2i where iis an integer greater than 1 and T is greater than the expected beatduration (in seconds).

A multi-resolution time-slicing is performed at step 20 forpreconditioning PPG data to be used as an input into collisions. Themulti-resolution time slicing is implemented in some embodiments viawindowing data into length WL=256 ms that is sufficient to capture thefastest beat rate expected where the PPG waveform sampling time is 16 ms(a fraction of 1/Ω), or other time that is generally different from theprimary power line period. As shown in FIG. 142, the incoming data issimultaneously windowed into lengths 2WL (i.e. 512 ms), 4WL (i.e., 1024ms) up to 8WL (i.e., 2048 ms), allowing capture of heart beats rangingfrom 300 bpm to 30 bpm.

Let such data streams be denoted by Φ(t,p,Wno) where Wno=1, 2, 3, and 4to corresponds to lengths WL, 2WL, 4WL and 8WL, respectively. Also,Φ(t,p,1) is subsumed within Φ(t,p,2), Φ(t,p,2) is subsumed withinΦ(t,p,3), and so on. An assumption is made that at least one beat occursin the interval indicated by one of the windows Wno. If the bpm rate isclose to the high end of the human bpm dynamic range then beats will bepresent in all time-windows. If, on the other hand, the bpm rate isclose to the low end of human dynamic range, it will be present in thelargest window corresponding to Wno=4. Also, per the Nyquist samplingtheorem, the sampling frequency is set to be equal to at least twice theexpected beat frequency. In various embodiments, the sampling frequencyis set to be significantly greater than the Nyquist frequency. Forexample, in one embodiment, the sampling rate is set to be 16 times thehighest expected beat frequency.

FIG. 143A illustrates this windowing of the PPG waveform 10 for a normalheart rate of 60 bpm, with the interval between beats of 1.0 seconds,15. Window lengths of W, 2W, 4W, and 8W, are 20, 25, 30, and 40respectively. An expanded display of window 50, corresponding to WL 20,shows the sampling intervals of every 16 milliseconds as vertical lines.FIG. 143B illustrates the PPG waveform 10 for a heart rate of 30 bpm,with the interval between beats of 2.0 seconds shown at 55, with thesame windowing and sampling interval indications as in FIG. 143A. FIG.143C, illustrates the PPG waveform 10 for a heart rate of 120 bpm, withthe interval between beats of 0.5 seconds shown at 65, with the samewindowing and sampling interval indications as in FIG. 143A.

It is further assumed that the beat event waveform shown in FIGS.143A-143C can change in shape, amplitude, phase, and width. Let eachdata structure corresponding to the window Φ(t,p,Wno) be denoted as afeature. Data is collected for window of size WL and that is calledFeature F(1,1). Data collection continues, and when window size 2WL isreached, all of that data is called Feature F(2,1), and so on forF(3,1), F(4,1) onwards.

Thus feature F(1,1) corresponds to data from time t=0 (or start of eventtrigger) to t=255 ms for Wno=1; feature F(1,2) corresponds to data fromtime t=256 ms to t=511 ms for Wno=1. Similarly, F(2,1) corresponds todata from t=0 to t=511 ms; Thus total feature set can be represented asF={F(1,1), F(1,2), . . . , F(1,8), F(2,1), F(2,2), . . . , F(2,4),F(3,1), F(3,2), F(4,1)}, 15 members. The total episodic window iscovered by EW/2048 ms spans of the largest window size. However, thewindows {Wno=1, Wno=2, . . . , Wno=4} are moved by t=64 ms orlength{Wno=1}/4 ms during the duration of episodic window. Hereafter,the processing is performed on all features in the set F.

From a logical view, PPG data is collected and sliced into time windowsto generate features, i.e., data is collected for a window of size 8WLand then sliced into a smaller window. As described above, in oneembodiment, the implementation follows a reverse procedure whereby datais collected for a window of size WL, then 2WL and so on.

FIG. 144 details conditioning of windowed PPG feature data, i.e., step20 shown in FIG. 141. Feature data from each time-window Φ(t,p,Wno) isup-sampled by interpolation to 4096 points at step 22. A Fouriertransform is performed on all features at step 24, followed by anoptional amplitude modulation at step 26 to increase signal-to-noiseratio. At step 28, the features are used to modulate a carrier kernel CKthat includes frequency components k, j, and m, (28) where, as anexample, k=3, m=3 and j=4089. Spectral energy collision computations areintended to amplify the k-components.

With reference to FIGS. 145 and 141, the conditioned feature data isthen entered into the collision engine 30. In the case of PPG, a singleZyoton Z is used. The Zyoton Z may be derived from the soliton familiesdescribed above. Also, all the features associated with the set F aresimultaneously introduced in the multiplexed collision engines 32, atstep 30 (FIG. 141). For example, feature F1 collides with Zyoton Z inCollision Engine 1, feature F2 collides with Zyoton Z in CollisionEngine 3, and so on. In some embodiments several different features arepipelined through a series of collision engines, each corresponding todata from a window with different accumulation length. A collision countas low as 16 may be used in the collision engine, assuming an SNR as lowas to 1:100, with window length of 64 data points. Renormalization ofthe modified zyoton between collisions determines the spectral energygain, computed as described above, but using k=3 components.

After completing the collisions NRSEG values associated with each of thefeatures are computed in step 35 (FIG. 141). In one embodiment, eachstep through step 30 yields 15 NRSEG values corresponding to differentconditioned features. The NRSEG values obtained from features withidentical window sizes are averaged and reduced to 4 levels. As anexample F(1,1), F(1,2), . . . F(1,8) are averaged to NRSEG_F1. F(2,1),F(2,2), . . . , F(2,4) are averaged to NRSEG_F2, and so on.

Beat event localization is performed in step 40. A test of monotonicityis performed by regressing NRSEG_F1, . . . , NRSEG_F4 against windowlength. The presence of a beat implies an increase over a thresholdvalue (e.g., 25% in one embodiment) in NRSEG numerical values. Also,presence of a beat in the smallest length window implies that the beatwill be seen a number times in all other longer length windows. ThusNRSEG_F4>NRSEG_F3>NRSEG_F2>NRSEG_F1. Also, NRSEG_F4 is some multiple ofNRSEG_F3, which is some multiple of NRSEG_F2, and so on. This multiplerelationship provides an estimate of the number of beats detected in thewindow interval corresponding to Wno=4. It is possible that an eventdoes not occur in some windows F(1,1), F(1,2), . . . F(1,8). Once anNRSEG change is detected in the averaged value corresponding to awindow_size, then individual values are examined to check the presenceof beats.

Projection includes the process whereby post-collision NRSEG values areused to determine the size of the smallest window size in which the beatcan be detected. Once a beat is detected and localized in time (based onthe window in which it was detected), it is added to a running count forthe current episodic window. The time window is then incremented by thelength of Wno/2, and the steps 22-28 in FIG. 144 is repeated. Only whena beat is detected in a new, later window where the beat start time isgreater than the start time of the previous beat, the beat counter isupdated at step 50. This is to allow for beats that are longer than thesliding interval and show up in multiple sliding time-slices.

Once the entire episodic interval has been covered, the accumulated beatrate is output to provide the heart rate. If the episodic interval isset to 10 seconds, the accumulated beat rate can be multiplied by 6 toget the heart rate per minute, in this example 60 bpm.

Sequences of numbers and waveforms are generally considered to bemathematical concepts and natural phenomena, respectively. Manipulationof a waveform, however, can be a limited, particular, useful applicationof the waveforms. For example, when amplitude modulation was inventeddecades ago, it described a particular manner in which one waveform,typically called a source waveform, could be used to modify anotherwaveform, typically called a carrier waveform, so that a modulatedwaveform resulting from the modulation can be transmitted over longdistances of up to hundreds or even thousands of miles. Frequencymodulation describes another particular manner of manipulating a carrierwaveform using a source waveform, that allowed for improvements insignal-to-noise ratio of the modulated waveform. Such techniques aregenerally not considered to be mathematical concepts or naturalphenomena, but rather are highly useful methods of achieving beneficialtechnical results.

Collision computing, according to various embodiments described herein,is also a limited, particular manner of manipulating waveforms toachieve highly beneficial results. The collision operation is not amodulation technique, at least because modulation is an invertibleoperation, i.e., the source waveform can be regenerated from a modulatedwaveform via the process of demodulation. Collision operation, ingeneral is non-invertible, however. This results from, at least in part,the bracketing and conditional interactions described above. Thesespecific operations, that distinguish the collision operation fromvarious modulation techniques and from other known waveform manipulationtechniques, also make the methods and systems for collision computinglimited and specialized techniques of waveform processing.

Unlike any generic operations such as data transmission and reception,unlike usual computer functions such as storage and access ofinformation, and unlike any mathematical or mental processes such ascomparing and categorizing information, the unconventional operationsdescribed herein are specifically orchestrated for selectivelyamplifying information represented within the frequency components of asignal. For example, some of the operations involve comparingfrequencies of waveform components where a permissible differencebetween the frequencies is selected according to the nature of thewaveform components in terms of the kind of information those componentsrepresent. Additional operations such as scaling, delay shifting, andphase rotation, are also particularly developed, non-generic operations.

Moreover, the waveforms used in the collision process are themselves ofa limited, particular kind. Specifically, these waveforms areco-dependent in terms of their respective velocities, and in terms of achange that one waveform generally causes in another during a collisiontherebetween. The process of creating such waveforms, though it maystart from various functions and/or number sequences, involves a carefulselection of a number of frequencies associated with several waveformcomponents. Unlike generic computer and database operations and typicalmathematical or mental processes, this selection is based on, at leastin part, the spectral properties of the analyte signals to be detectedand/or measured, or an event or anomaly to be detected and/orcharacterized, as described above. As such, the methods and systems forsynthesizing these co-dependent waveforms also involve unconventional,limited, and particularized operations generally involving analysis ofspectral properties of signals.

While glucose (and other analytes) occur naturally in many living thingsincluding humans, accurate knowledge of the presence, absence, quantity,and/or concentration of these analytes is neither a natural phenomenonnor can such knowledge be obtained by mere mental processing. Typically,physical samples (e.g., blood) and/or signals (e.g., reflected ortransmitted radiation, electromagnetic pulses, etc.) are obtained. Thisinformation is then processed and analyzed to determine the presence,absence, quantity, and/or concentration of the analyte. Theseinformation processing techniques, however, are generally not consideredto be mental processes and/or natural phenomena. Collision computingdescribed herein and implemented in various embodiments is a new,specialized technique to that end.

It is clear that there are many ways to configure the device and/orsystem components, interfaces, communication links, and methodsdescribed herein. The disclosed methods, devices, and systems can bedeployed on convenient processor platforms, including network servers,personal and portable computers, and/or other processing platforms.Other platforms can be contemplated as processing capabilities improve,including personal digital assistants, computerized watches, cellularphones and/or other portable devices. The disclosed methods and systemscan be integrated with known network management systems and methods. Thedisclosed methods and systems can operate as an SNMP agent, and can beconfigured with the IP address of a remote machine running a conformantmanagement platform. Therefore, the scope of the disclosed methods andsystems are not limited by the examples given herein, but can includethe full scope of the claims and their legal equivalents.

The methods, devices, and systems described herein are not limited to aparticular hardware or software configuration, and may findapplicability in many computing or processing environments. The methods,devices, and systems can be implemented in hardware or software, or acombination of hardware and software. The methods, devices, and systemscan be implemented in one or more computer programs, where a computerprogram can be understood to include one or more processor executableinstructions. The computer program(s) can execute on one or moreprogrammable processing elements or machines, and can be stored on oneor more storage medium readable by the processor (including volatile andnon-volatile memory and/or storage elements), one or more input devices,and/or one or more output devices. The processing elements/machines thuscan access one or more input devices to obtain input data, and canaccess one or more output devices to communicate output data. The inputand/or output devices can include one or more of the following: RandomAccess Memory (RAM), Redundant Array of Independent Disks (RAID), floppydrive, CD, DVD, magnetic disk, internal hard drive, external hard drive,memory stick, or other storage device capable of being accessed by aprocessing element as provided herein, where such aforementionedexamples are not exhaustive, and are for illustration and notlimitation.

The computer program(s) can be implemented using one or more high levelprocedural or object-oriented programming languages to communicate witha computer system; however, the program(s) can be implemented inassembly or machine language, if desired. The language can be compiledor interpreted.

As provided herein, the processor(s) and/or processing elements can thusbe embedded in one or more devices that can be operated independently ortogether in a networked environment, where the network can include, forexample, a Local Area Network (LAN), wide area network (WAN), and/or caninclude an intranet and/or the Internet and/or another network. Thenetwork(s) can be wired or wireless or a combination thereof and can useone or more communication protocols to facilitate communication betweenthe different processors/processing elements. The processors can beconfigured for distributed processing and can utilize, in someembodiments, a client-server model as needed. Accordingly, the methods,devices, and systems can utilize multiple processors and/or processordevices, and the processor/processing element instructions can bedivided amongst such single or multiple processor/devices/processingelements.

The device(s) or computer systems that integrate with theprocessor(s)/processing element(s) can include, for example, a personalcomputer(s), workstation (e.g., Dell, HP), personal digital assistant(PDA), handheld device such as cellular telephone, laptop, handheld, oranother device capable of being integrated with a processor(s) that canoperate as provided herein. Accordingly, the devices provided herein arenot exhaustive and are provided for illustration and not limitation.

References to “a processor”, or “a processing element,” “the processor,”and “the processing element” can be understood to include one or moremicroprocessors that can communicate in a stand-alone and/or adistributed environment(s), and can thus can be configured tocommunicate via wired or wireless communication with other processors,where such one or more processor can be configured to operate on one ormore processor/processing elements-controlled devices that can besimilar or different devices. Use of such “microprocessor,” “processor,”or “processing element” terminology can thus also be understood toinclude a central processing unit, an arithmetic logic unit, anapplication-specific integrated circuit (IC), and/or a task engine, withsuch examples provided for illustration and not limitation.

Furthermore, references to memory, unless otherwise specified, caninclude one or more processor-readable and accessible memory elementsand/or components that can be internal to the processor-controlleddevice, external to the processor-controlled device, and/or can beaccessed via a wired or wireless network using a variety ofcommunication protocols, and unless otherwise specified, can be arrangedto include a combination of external and internal memory devices, wheresuch memory can be contiguous and/or partitioned based on theapplication. For example, the memory can be a flash drive, a computerdisc, CD/DVD, distributed memory, etc. References to structures includelinks, queues, graphs, trees, and such structures are provided forillustration and not limitation. References herein to instructions orexecutable instructions, in accordance with the above, can be understoodto include programmable hardware.

Although the methods and systems have been described relative tospecific embodiments thereof, they are not so limited. As such, manymodifications and variations may become apparent in light of the aboveteachings. Many additional changes in the details, materials, andarrangement of parts, herein described and illustrated, can be made bythose skilled in the art. Accordingly, it will be understood that themethods, devices, and systems provided herein are not to be limited tothe embodiments disclosed herein, can include practices otherwise thanspecifically described, and are to be interpreted as broadly as allowedunder the law.

What is claimed is:
 1. A method of quantitating an analyte, the methodcomprising: receiving from an uncharacterized sample an energy changevalue to be mapped, the energy change value corresponding to anuncharacterized sample; mapping, via a first processor, the energychange value to be mapped to a quantity of an analyte in theuncharacterized sample, via an individual projector curve associating:(i) energy change values obtained from a synthetic reference system toanalyte quantities of the reference system, and (ii) energy changevalues obtained from a non-synthetic reference system to the analytequantities of the reference system.
 2. The method of claim 1, furthercomprising: computing a representative absorption gradient (AG) using afirst set of energy change values corresponding to a first feature pair,each energy change value in the first set corresponding to a respectivepath of radiation through a medium to be analyzed; selecting theindividual projector curve from a plurality of projector curves usingthe representative gradient value associated with the first featurepair; and determining a quantity of an analyte using the selectedindividual projector curve, the energy change value to be mapped being arepresentative energy change value associated with the first featurepair.
 3. The method of claim 2, wherein the representative gradientvalue comprises a normalized AG (NAG), the method further comprising:weighing the representative gradient associated with the first featurepair by a weight associated with the first feature pair, to obtain theNAG.
 4. The method of claim 2, wherein computing the representativeenergy change value comprises weighting one energy change value from thefirst set of energy change values by a weight associated with the firstfeature pair.
 5. The method of claim 2, wherein a plurality of featurepairs comprises the first feature pair, the method further comprising:generating a set of acceptable feature pairs from the plurality offeature pairs; for each feature pair in the set of acceptable featurepairs computing a respective absorption gradient (AG) using a respectiveset of energy change values corresponding to the feature pair; computingthe representative AG value as an average of the respective AGsassociated with each of the acceptable feature pairs.
 6. The method ofclaim 5, wherein generating the set of acceptable feature pairscomprises testing for each feature pair in the plurality of featurepairs monotonicity of the corresponding set of energy change valuesacross a plurality of illumination states.
 7. The method of claim 5,wherein computing the AG for each acceptable feature pair comprises:determining a slope of a regression of the corresponding set of energychange values with respect to the illumination states, the illuminationstates being ordered such that successive illumination states representmonotonically changing distance between the source and at least onedetector.
 8. The method of claim 5, further comprising, prior tocomputing the average: normalizing each of the AGs corresponding to theacceptable feature pairs using a weight associated with thecorresponding acceptable feature pair.
 9. The method of claim 5 whereincomputing the representative energy change value comprises: for eachacceptable feature pair, selecting one energy change value from therespective set of energy change values; weighting for each acceptablefeature pair, the selected energy change value by a weight associatedwith the acceptable feature pair; and setting an average of the weightedenergy change values as the representative energy change value.
 10. Themethod of claim 1, wherein: the uncharacterized sample comprises aportion of tissue; and the analyte comprise glucose.
 11. The method ofclaim 1, wherein the energy change comprises one of energy gain andenergy loss.
 12. A system of quantitating an analyte, the systemcomprising: a first processor; and a first memory in electricalcommunication with the first processor, the first memory comprisinginstructions which, when executed by a processing unit comprising atleast one of the first processor and a second processor, and inelectronic communication with a memory module comprising at least one ofthe first memory and a second memory, program the processing unit to:receive an energy change value to be mapped, the energy change valuecorresponding to an uncharacterized sample; and map the energy changevalue to be mapped to a quantity of an analyte in the uncharacterizedsample, via an individual projector curve associating: (i) energy changevalues obtained from a synthetic reference system to analyte quantitiesof the reference system, and (ii) energy change values obtained from anon-synthetic reference system to the analyte quantities of thereference system.
 13. The system of claim 12, wherein the instructionsfurther program the processing unit to: compute a representativeabsorption gradient (AG) using a first set of energy change valuescorresponding to a first feature pair, each energy change value in thefirst set corresponding to a respective path of radiation through amedium to be analyzed; select the individual projector curve from aplurality of projector curves using the representative gradient valueassociated with the first feature pair; and determine a quantity of ananalyte using the selected individual projector curve, the energy changevalue to be mapped being a representative energy change value associatedwith the first feature pair.
 14. The system of claim 13, wherein therepresentative gradient value comprises a normalized AG (NAG), whereinthe instructions further program the processing unit to: weigh therepresentative gradient associated with the first feature pair by aweight associate with the first feature pair, to obtain the NAG.
 15. Thesystem of claim 13, wherein to compute the representative energy changevalue, the instructions further program the processing unit to weightone energy change value from the first set of energy change values by aweight associated with the first feature pair.
 16. The system of claim13, wherein a plurality of feature pairs comprises the first featurepair, wherein the instructions further program the processing unit to:generate a set of acceptable feature pairs from the plurality of featurepairs; for each feature pair in the set of acceptable feature pairscompute a respective absorption gradient (AG) using a respective set ofenergy change values corresponding to the feature pair; compute therepresentative AG value as an average of the respective AGs associatedwith each of the acceptable feature pairs.
 17. The system of claim 16,wherein to generate the set of acceptable feature pairs, theinstructions further program the processing unit to test for eachfeature pair in the plurality of feature pairs monotonicity of thecorresponding set of energy change values across a plurality ofillumination states.
 18. The system of claim 16, wherein to compute theAG for each acceptable feature pair, the instructions further programthe processing unit to: determine a slope of a regression of thecorresponding set of energy change values with respect to theillumination states, the illumination states being ordered such thatsuccessive illumination states represent monotonically changing distancebetween the source and at least one detector.
 19. The system of claim16, wherein the instructions further program the processing unit to:prior to computing the average, normalize each of the AGs correspondingto the acceptable feature pairs using a weight associated with thecorresponding acceptable feature pair.
 20. The system of claim 16,wherein to compute the representative energy change value, theinstructions further program the processing unit to: for each acceptablefeature pair, select one energy change value from the respective set ofenergy change values; weight for each acceptable feature pair, theselected energy change value by a weight associated with the acceptablefeature pair; and set an average of the weighted energy change values asthe representative energy change value.
 21. The system of claim 12,wherein: the uncharacterized sample comprises a portion of tissue; andthe analyte comprises glucose.
 22. The system of claim 12, wherein theenergy change comprises on of energy gain and energy loss.